2.1 Lexically Licensed NI

Usually or always, lexically licensed NI occurs as an alternative to overt instantiation.Footnote ³ Consider the English verb contribute. Since the object is optionally INI and the PP complement is optionally DNI, one has paradigmatic examples like (10).Footnote ⁴

1. 1. a. I will contribute ten dollars to your campaign.

   2. b. I will contribute _[something] to your campaign.

   3. c. I will contribute ten dollars _[to you know what].

   4. d. I will contribute _[something] _[to you know what].

To account grammatically for the kind of variation displayed in (10) one could posit four distinct listemes contribute. That approach would fail to capture the generalization of optionality in an explicit fashion. Instead, we will assume that the NI potential associated with any given argument of a predicate is directly captured in the argument structure of the respective lexeme. In other words, a word like contribute will be specified with the following argument structure and partially underspecified constraints on argument indices, as informally depicted in (11) and fully developed in Section 3.2.

1. (11) Argument structure for contribute

   $⟨{\text{NP}}_{x:\mathrm{\neg }\text{NI}},{\text{NP}}_{y:\mathrm{\neg }\text{DNI}},{\text{PP}}_{z:\mathrm{\neg }\text{INI}}⟩$

The intuition is that contribute selects a list of three arguments, the first of which, in a finite clause, is an NP that cannot be NI (i.e. its referent must be introduced by an overt subject phrase). The verb contribute in addition subcategorizes for an NP direct object that cannot be DNI (i.e. it must either be referential or INI), and an oblique that cannot be INI (i.e. it must either be referential or DNI). Thus, if the latter two arguments are not overtly realized, they are required to be interpreted existentially or anaphorically, respectively. However, there are a variety of contexts that interact with a lexeme’s argument structure and license otherwise illicit NI patterns.

2.2 Contextually Licensed NI

There are cases in which features of the discourse context, including narrative context and shared background knowledge, allow a predicator to exhibit NI potential it does not possess inherently. The verb pull does not, in general, license DNI, as illustrated in the following excerpt from a hearing of a commission of the US Congress.

1. (12)

   ${}^{@}$ Mr. Blanton: Had your little girl pulled this fire-alarm box that you know of?

   Mr. Puliam: No, sir; and nobody had seen her pull *(it).

   Mr. Blanton: And they just suspected she had pulled *(it)?

   Mr. Puliam: The fire-alarm box had been pulled and my children were seen around there.

   Mr. Blanton: And the child could have pulled *(it)?

   Mr. Puliam: Yes, sir.

   Mr. Blanton: And there are some 66,000 other children in the District who could have pulled *(it)?

However, in a situation of sufficient immediacy and salience, the object of a verb like pull or push, which does not inherently license DNI, may remain implicit. (13) and (14) illustrate (object and subject) DNI of this kind, which we dub Accessibility DNI.

1. 1. a. I leaped to my feet and stumbled toward her. My fingers grabbed for the deadly necklace. I pulled $\mathrm{\varnothing }$ with all my strength. Snap! (Stine, Reference Stineundated)

   2. b. Ernesto pointed again to the rocks. “Learn not to push $\mathrm{\varnothing }$ before the right moment,” he said. (Stine, Reference Stein1958)

   3. c. Suddenly the boulder was rocking and Tola Beg pushed $\mathrm{\varnothing }$ hard, pushed $\mathrm{\varnothing }$ with all the strength he had in his old body and with all the strength he had in his mind. (L’Amour, Reference L’Amour2001, 36)

1. 1. a. So, how’s Julia?

      $\mathrm{\varnothing }$ Broke her arm, and hit her head pretty badly. She’s in the hospital for observation. (Crichton, Reference Crichton2002, 157)

   2. b. ${}^{@}$ (Your guy gets to the plate, kicks in the sand, knocks his shoes with the bat. He always does that.) $\mathrm{\varnothing }$ Takes his stance. $\mathrm{\varnothing }$ Gets comfortable. $\mathrm{\varnothing }$ Looks at the pitcher for the first time.

   3. c. ${}^{@}$ Announcer: And he’s behind Lehtonen, 3 seconds left, $\mathrm{\varnothing }$ passes it to Sutton, and THE THRASHERS WIN 2–0.

We take the key concept at work in licensing this kind of NI to be the accessibility of an intended referent (Ariel, Reference Ariel, Sanders, Schilperoord and Spooren2001; Gregory & Michaelis, Reference Gregory and Michaelis2001). Accessibility is conceived as a gradient property: the degree to which “the speaker can predict or could have predicted that a particular linguistic item will or would occur in a particular position within a sentence” (Prince, Reference Prince1981a, 226).

Ruppenhofer & Michaelis (Reference Ruppenhofer and Michaelis2010) note that generic, including habitual, aspect can also license INI of the direct object of a simple transitive verb, while this is not possible under other circumstances. Consider for example the contrast in (15). Ruppenhofer and Michaelis refer to such cases as dispositional INI.

1. 1. a. * The cops arrested $\mathrm{\varnothing }$ last night.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer, Michaelis, Bourns and Myers2014, 159)

   2. b. Sure, the cops arrest $\mathrm{\varnothing }$ when they can, but it’s always in small amounts.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer, Michaelis, Bourns and Myers2014, 159)

As we discuss in what follows, we adopt the dispositional operator proposed by Boneh (Reference Boneh2019), which yields habitual, generic, or disposition readings depending on circumstances. Disposition attributions are statements that ascribe to an entity an inherent property that may remain unrealized unless the right conditions obtain. Dispositional DNI is not limited to direct objects, as the attested datum in (16) shows.

1. (16) ${}^{@}$ He or she is a philanthropist and gives $\mathrm{\varnothing }\mathrm{\varnothing }$ whenever asked for assistance.

Another contextual licensor of NI is the instructional imperative, which allows the DNI suppression of an object in imperative constructions expressing instructions. This is illustrated in (17). In this genre, the context must be such that the theme under discussion is the topic of the utterance, which assures the possibility of a DNI interpretation.

1. 1. a. Method: Blend all the ingredients in an electric blender. Serve $\mathrm{\varnothing }$ cold.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 106)

   2. b. Chill ${\mathrm{\varnothing }}_i$ before serving ${\mathrm{\varnothing }}_i$.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 159)

   3. c. In a bowl, toss ${\mathrm{\varnothing }}_i$ with salt and set ${\mathrm{\varnothing }}_i$ aside.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer, Michaelis, Bourns and Myers2014, 72)

   4. d. In a skillet, sauté ${\mathrm{\varnothing }}_i$ until browned ${\mathrm{\varnothing }}_i$ but not crisp ${\mathrm{\varnothing }}_i$.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer, Michaelis, Bourns and Myers2014, 72)

Ruppenhofer & Michaelis (Reference Ruppenhofer and Michaelis2010) observe that NI is licensed by several other genres, such as “labelese,” diary style, sports reporting (“match reports”), and certain nonquotative verbs used quotatively. For all of these, NI is of the deictic/anaphoric – that is, DNI, variety and in some cases targets erstwhile subjects. Example (18a) illustrates labelese and (18b, c) illustrate the diary genre.Footnote ⁵

1. 1. a. $\mathrm{\varnothing }$ Contains alcohol.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 160)

   2. b. $\mathrm{\varnothing }$ Woke up, $\mathrm{\varnothing }$ fought with Marge... $\mathrm{\varnothing }$ ate Guatemalan insanity peppers...

      [COCA, TV 1997]

One final instance of contextual NI that we will consider is observed in the omission of the oblique argument in short passives, illustrated in the minimal pair in (19). The agent of fed is unexpressed in (19b). We will argue that whether the oblique argument is overtly realized depends on the cognitive status of the demoted agent.

1. 1. a. The iguanas were properly fed by Robin.

   2. b. The iguanas were properly fed $\mathrm{\varnothing }$.

2.3 Constructionally Bound Implicit Arguments

Whereas NI involves implicit arguments whose semantic value is determined directly from context independently of anything else in the logical structure of the sentence, there are also cases where implicit arguments derive part of their semantic value from elsewhere in the linguistic representation, and therefore are more syntactically active. Such implicit arguments resemble NI but differ from it in that their interpretation is constrained by some aspect of the grammar, rather than by discourse context. This is the case of controlled pro examples like (20a,b), which are co-referential with a structurally higher argument, and other constructions such as implicit subjects of dangling participles like (20c), as well as imperative subjects like (20d).

1. 1. a. I [made [the top]${}_x$ [${\mathrm{\varnothing }}_x$ go into the cup]].

   2. b. I ${}_x$ love [${\mathrm{\varnothing }}_x$ to play this game].

   3. c. ${\mathrm{\varnothing }}_x$ Sitting on a park bench, Sam ${}_x$ watched the kids play.

   4. d. $\mathrm{\varnothing }$ Get me another cup please.

Each of the constructions responsible for governing the reference of these pro arguments imposes a different constraint. For example, in (20c) the implicit subject is required to be the subject of the matrix, whereas in (20d) the subject is assigned the same semantic content as the pronoun you, and is omitted.

Remarkably, such implicit pro arguments can be displaced by a construction. For instance, in (21a) the object of please is extracted and linked to the implicit inverted subject of the imperative. Analogously, in (21b) the pro object is extracted to the subject position in the arg-st. In (21c) the implicit object of fed is passivized, promoted to the subject argument of the dangling participle, and in (21d) the implicit object is extracted from the object phrase and corresponds to the object of the preposition of. Finally, in (21e) a pro theme of won can be extracted, and co-indexed with the nominal head prize.

1. 1. a. Don’t ${\mathrm{\varnothing }}_x$ be so hard to please _ ${}_x$.

   2. b. ${\mathrm{\varnothing }}_x$ Being especially easy to talk to _ ${}_x$, Pat ${}_x$ was able to escape being laid off.

   3. c. If ${\mathrm{\varnothing }}_x$ properly fed, Iguanas ${}_x$ can live for a long time.

   4. d. If ${\mathrm{\varnothing }}_x$ taken good care of _ ${}_x$, Iguanas ${}_x$ can live for a long time.

   5. e. The prize ${}_x$ which ${}_x/{\mathrm{\varnothing }}_x$ I thought you won _ ${}_x$ was this one.

Such data suggest that implicit pro arguments can still participate in standard alternations, like their overt counterparts. This contrasts with NI, which disallows displacement as illustrated in (22). Thus, (22a) cannot be interpreted as a content question (only as a polar question), and (22b) is illicit.

1. 1. a. *${\mathrm{\varnothing }}_x$ Did Robin win _ ${}_x$?

      ($\ne$ ‘What ${}_x$ did Robin win _ ${}_x$?’)

   2. b. *${\mathrm{\varnothing }}_x$ Is easy to talk to _ ${}_x$.

      (cf. ‘Sam ${}_x$ is easy to talk to _ ${}_x$.)

We also assume that arbitrary pro constructions like those in (23) also involve a pro argument rather than an NI argument, given that such implicit arbitrary referents have a generic import. We assume this import comes from being bound to a covert generic quantifier that is introduced via a lexical rule.Footnote ⁶

1. 1. a. $\mathrm{\varnothing }$ To err is human.

   2. b. It is forbidden $\mathrm{\varnothing }$ to smoke.

   3. c. The Titanic was easier $\mathrm{\varnothing }$ to sink than anyone imagined.

Bhatt and Pancheva (Reference Bhatt and Pancheva2006) point out that the fact that some implicit arguments have syntactic effects, while others don’t, is theoretically disturbing, and the line between the two classes is not agreed upon. In our view, the relation between NI arguments and pro arguments is the one summed up in (24).

1. (24) The NI/pro Generalization:

$\bullet$ NI arguments are not bound in the logical structure of the sentence.

$\bullet$ Pro arguments are bound in the logical structure of the sentence.

Landau (Reference Landau2010) makes a distinction between Strong Implicit Argument (SIA) and Weak Implicit Argument (WIA), but the empirical basis for such a categorization is problematic (Michelioudakis, Reference Michelioudakis, Bárány, Biberauer, Douglas and Vikner2021). Consider the supposed contrast in (25). Landau’s claim is that the passive agent of played is a WIA because it is not present in syntactic structure, and therefore shoeless cannot be predicated of it.

1. 1. a. The game was played [pro wearing no shoes].

   2. b. *The game was played shoeless.

      (Landau, Reference Landau2010, 360)

We note that a verbatim Google search on 9/5/21 for was played shoeless produced many examples like “The game was played shoeless,” “Previous shot was played shoeless and sockless from a water hazard,” and “But the entire regional qualification process in Mexico was played shoeless.” Even more frequent is the string was played barefoot, yielding examples like (26).Footnote ⁷

1. (26) ${}^{@}$ Players will take the soccer fields with no shoes. The inaugural event held in 2017 was played barefoot, with the money going to children without shoes through Soles 4 Souls.

Landau (Reference Landau2010) relies on well-known contrasts such as (27) to argue for a distinction between WIA and SIA. But the verb eat is arguably ambiguous between an intransitive verb denoting a social event, and a transitive verb denoting a manner of consumption. See Glass (Reference Glass2021) for corpus evidence suggesting that such verbs omit their objects more often in the communities where they are more strongly associated with a routine. If so, then the oddness of (26b) follows from attaching an adjective to an intransitive verb.

1. 1. a. John ate (the meat).

   2. b. John ate *(the meat) raw.

This view is also consistent with the fact that the transitive use of eat seems to allow object NI in certain constructions:

1. (28) These are just a few of the people who are eating $\mathrm{\varnothing }$ raw. ... Each person has different reasons for eating raw.

   [COCA 2005 MAG TotalHealth]

3.1 Sign-Based Construction Grammar

Sign-Based Construction Grammar takes all linguistic objects like words and phrases to be bundles of phonological, morphosyntactic, semantic, and pragmatic information – that is, Sausurean signs. Like its predecessors, SBCG seeks to explicitly characterize the infinite set of signs that constitutes a language in a declarative, constraint-based fashion. Signs are modeled as typed feature structures, represented as Attribute Value Matrices (AVMs) like the one in (29).

1. (29)

   Linguistics 1

   

An AVM is a set of attribute–value pairs, representing a function from a set of attributes to a set of types of feature structure. For example, the AVM in (29) denotes a set of feature structures typed as sign, and as such it comes with a set of attribute–value pairs each of which specifies a different kind of information. A sign therefore contains information about sound (phon), morphological form (form), syntax (syn), meaning (sem), and context ( cntxt). Attributes are written in small caps and types are written in lowercase italics. Unlike the complex feature structures such as (29), represented by AVMs, other feature structure types are atomic. Examples are accusative, finite, “ $-$,” and “ $+$.”

Signs are arranged in a multiple-inheritance hierarchy, as illustrated in (30), whereby all the subtypes of sign inherit the attribute–value pairs that are appropriate for signs, as shown in (29), as well as additional constraints distinguishing the subtypes.

1. (30)

   

   Linguistics 2Long description

   The labeled tree diagram depicts a hierarchical structure of linguistic categories. The top node is sign, which branches into lexical-sign and expression. Expression divides into word and phrase. Lexical-sign leads to lexeme, which connects to v dash l x m followed by an ellipsis. The v dash l x m node further splits into intr dash l x m, p t v dash l x m, and drv dash l x m, ending with another ellipsis.

For example, only signs of type expression, whose subtypes include the types word and phrase, but not lexeme, are allowed in syntactic constructions (preventing lexemes from appearing in syntax), and only signs of the type lexical-sign are allowed in lexical rules. More specifically, morphological derivation rules map signs of type lexeme to signs of type lexeme, and inflectional rules map signs of type lexeme to signs of type word. The fact that the type word inherits the properties of both lexical-sign and expression illustrates the multiple inheritance property. The type lexeme is the supertype of a rich ontology of lexemes, organized in terms of cross-cutting classes (intr-lxm for intransitive lexemes, ptv-lxm for prepositional transitive, dtv-lxm for ditransitive lexemes, etc.), called the hierarchical lexicon (Flickinger, Reference Flickinger1987). Analogous subhierarchies exist for nonverbal lexeme classes, which are not shown here due to space limitations. See Sag (Reference Sag, Boas and Sag2012) for a more detailed discussion. For example, in (31), we show the lexeme for contribute, a subtype of pvt-lxm, as it is listed in the lexicon.

1. (31)

   

   Linguistics 3Long description

   The labeled feature structure diagram titled thirty-one represents the lexical entry for contribute dash l x m. The top-level brackets contain two attributes: F O R M and S E M. The F O R M attribute maps to the angled bracket value contribute. The S E M attribute includes a nested structure with two parts: I N D E X, labeled S, and F R A M E S, which maps to an angled bracket structure labeled contribute dash f r. Inside contribute dash f r is S I T, also labeled S.

As in HPSG, signs of type lexical-sign introduce one additional feature to what we see in (31), called arg-st, which takes lists of signs as its value, and encodes the number, type, and order of arguments that a given sign subcategorizes, regardless of whether such arguments are realized in situ or ex situ, or remain covert, including those interpreted via NI. The members of arg-st appear in order of increasing obliqueness, reflecting Keenan and Comrie’s Accessibility Hierarchy (Keenan & Comrie, Reference Keenan and Comrie1977). Sag, Wasow, and Bender (Reference Sag, Wasow and Bender2003, 241) and Ginzburg and Sag (Reference Ginzburg and Sag2000, 20-22), general constraints over classes and subclasses of lexemes are responsible for instantiating arg-st values in lexemes. In (32), we provide the constraints that are relevant for prepositional transitive verbal lexemes like contribute in (31), which we assume are also responsible for binding the indices in frames to the appropriate arguments. Generally, constraints like (32) are of the form $\tau \Rightarrow \varphi$ (where $\tau$ is some type and $\varphi$ is an AVM feature structure description) and impose restrictions on lexical classes, syntactic structure, semantic composition, phonological structure, morphology, and so on. Here we assume that the lexeme type contribute-lxm (among others) is a subtype of prepositional-transitive-verb-[to]-lexeme (abbreviated as ptv[to]-lxm), which in turn is a subtype of a larger family of lexeme types, ptv-lxm. Each of these types imposes constraints that vary in granularity, and subtypes inherit all the constraints of their supertypes.

1. (32)

   

   Linguistics 4Long description

   Two boxed lexical entries marked a and b. In part a, the entry is labeled ptv dash l x m and maps to a feature structure with A R G dash S T containing N P square bracket index X square bracket, N P square bracket index Y square bracket, and P P square bracket index Z square bracket. The S E M attribute includes F R A M E S, which contains F E S mapping to angled brackets with X, Y, and Z, followed by an ellipsis. In part b, the entry is labeled ptv square bracket to square bracket dash l x m and maps to an A R G dash S T structure that includes a placeholder ellipsis and a value labeled M A R K I N G mapped to to.

In words, (32a) states that every sign of the type ptv-lxm bears the subcategorization frame $⟨$ NP ${}_x$, NP ${}_y$, PP ${}_z⟩$.Footnote ⁸ Note that f(rame-)e(lement)s values are lists of indices,Footnote ⁹ while arg-st values are lists of signs. The constraint in (32a) thus specifies the value of arg-st and f(rame-)e(lement)s of all verbal lexemes that correspond to prepositional transitive verbs, or more technically, resolves the underspecified values of arg-st and fes for all lexemes typed as instances of ptv-lxm. The constraint in (32b) states that the ptv[to]-lxm subtype of ptv-lxm further requires that the most oblique argument be marked with the preposition to. Other sister types of ptv[to]-lxm impose different marking patterns, all of which share the constraints imposed by ptv-lxm. In the case of the contribute-lxm sign in (31), this results in the lexeme shown in (33). The result is a lexeme that selects a subject NP, a direct object, and an oblique object, as seen in (33).

1. (33)

   

   Linguistics 5Long description

   The boxed typed feature structure for contribute-lxm, representing a lexical item. The F O R M field contains the angled-bracketed value contribute. The I N D E X field contains the value S. The S E M field contains a nested F R A M E S structure with contribute-fr as the frame type, S I T with value S, F E S containing a triple ⟨X, Y, Z⟩ in angle brackets. The A R G - S T (argument structure) field contains a list of three elements as follows. N P with I N D E X Z, N P with I N D E X Y, P P with a nested structure. M A R K I N G with value to, I N D E X Z.

Semantically, the verb denotes a predication of the form $contribute(s,x,y,z)$, if rendered in a more standard first-order logic notation, which we encode in terms of a frame. In general, we have the correspondence in (34), for any given frame predicate name $P$ with $n$ arguments (i.e. frame elements).

1. (34) $P(s,x_1,...,x_n)$    is encoded as  $\left[\begin{array}{ll}P\text{-}fr& \\ \text{SIT}& S\\ \text{FES}& ⟨X_1,...,X_n⟩\end{array}\right]$

In (32a), the order of elements in the arg-st value is the same as the order of the elements in the fes value of the first frame. This co-alignment is dictated by the fact that we do not distinguish individual frame elements by naming them. The fact that we order the frame elements to match the order of syntactic obliqueness may give the impression of a tacit assumption that the syntactic properties of an argument determine its semantic properties. Nothing of the sort is intended. The ordering of the fes value to match that of the arg-st value is simply a matter of notational necessity. On the contrary, we are aware of the long tradition of serious efforts to derive the principle syntactic properties of a predicate’s arguments from its semantics – that is, linking theory (Bresnan & Zaenen, Reference Bresnan, Zaenen, Dziwirek, Farrell and Mejías-Bikandi1990; Goldberg, Reference Goldberg2019; Grimshaw, Reference Grimshaw1990; Levin, Reference Levin1993; Levin, Reference Levin1985). For a theory of argument linking particularly appropriate to the present approach see Davis (Reference Davis2001), Koenig and Davis (Reference Koenig, Davis and Müller2003, Reference Koenig and Davis2006), and Davis, Koenig, and Wechsler (Reference Davis, Koenig, Wechsler, Müller, Abeillé, Borsley and Koenig2021).

There are various other lexemic constraints at work, such as the one in (35). In the case of English, the first member of a verbal arg-st list is the external argument (xarg), which has a number of special properties, as described in what follows. Thus, (35) applies to all verbal lexemes to state their part-of-speech and to single out the first member of the arg-st list as being the external argument.

1. (35)

   

   Linguistics 6Long description

   The boxed typed feature structure representing v-l x m, a verb lexical type. The S Y N field contains a nested C A T structure with three subfields as follows. Verb as the category, X A R G with value K, L I D with value L. The S E M field includes F R A M E S with value L. The A R G - S T field is an angled-bracketed list beginning with K followed by ellipsis, indicating additional unspecified arguments.

Italicized capitals are variables over feature structures, and so the presence of two such occurrences in (35) means that the value of xarg is the same sign as the first member of arg-st. The members of a frames list always form a single-rooted tree with respect to the binary relation according to which one frame serves, via its label value, as an argument of another frame. The initial frame of a list is the root of the tree. The value of the feature l(exical)id(entity), on the other hand, is the entire list of frames of a lexeme. In a headed phrase the lid is visible at every level of “projection,” and thus allows for the selection of a complement to be constrained by the identity of the lexical head, as in rely on/*in her, trust *on/in her.

The sign singled out by xarg has a number of special properties in English. This is the only argument that can bear nominative case, is suppressed in passive although optionally available as an oblique complement headed by the preposition by, appears immediately postverbally in inverted clauses, serves as the target of control and raising, binds the pronominal subject of a sentence tag (36a), participates in the binding relation between an dangling participle subject and an element of the main clause (36b,c), etcetera. The last two properties illustrate the fact that the xarg is the only argument that can participate in a dependency with an item outside its clause.Footnote ¹⁰

1. 1. a. The guests ${}_x$ left, didn’t they ${}_x$?

   2. b. ${\mathrm{\varnothing }}_x$ Having caught sight of each other ${}_x$, the kids ${}_x$ started laughing.

   3. c. Which kid ${}_x$ did you say that – with his ${}_x$ parents out of town – _ ${}_x$ would not be too hard to convince _ ${}_x$ to host a party?

The arg-st feature is restricted to lexical signs – that is, lexemes and words – but the xarg, as a category feature (analogous to the head feature of HPSG) is visible at all levels of a headed phrase. For completeness, the effect of applying (35) to (33) is shown in (37). In reality, all constraints apply simultaneously, and therefore (37) is the result of simultaneously combining (31), (32), and (35). The notation $K$: $\varphi$ means that the value of the variable $K$ has at least the information described by $\varphi$. Thus, the value of xarg is the same sign that appears at the beginning of the arg-st list, and is required to be an NP bearing index $X$.

1. (37)

   

   Linguistics 7Long description

   The typed linguistic structure diagram labeled contribute l x m displays the form as contribute. The s y n section specifies category verb, with X A R G K and L I D L, and an index S. The s e m section lists frames labeled L containing contribute f r with S I T s and F E S comprising X, Y, and Z. The a r g s t section lists K as N P with index X, another N P with index Y, and a P P with marking to and index Z.

Although the arg-st contains the argument structure information of a lexical expression, it says nothing about how each particular argument is to be realized. Those elements of arg-st that appear in the feature val(ence) are to be locally realized, and those that appear in gap are to be realized ex situ (e.g., clefts, topicalization, wh-interrogatives, etc.). The mapping between arg-st and these syn features is achieved by the Argument Realization Principle (ARP) as shown provisionally in (38), adapted from Ginzburg and Sag (Reference Ginzburg and Sag2000, 214) to SBCG. Here, val and gap are lists of signs, like arg-st.

1. (38)

   

   Linguistics 8Long description

   The typed linguistic structure diagram labeled Argument Realization Principle Construction with lexical sign and provisional in brackets displays word mapping to a structure with s y n containing v a l L 1 and g a p L 2, and a r g s t listed as L 1 circle L 2. Bracketed notation is used to organize syntactic and argument structure information hierarchically.

In (38) the arg-st list is nondeterministically split into two sublists using the sequence union relation ‘ $◯$’ (Kathol, Reference Kathol, Culicover and Postal2001; Reape, Reference Reape, Bunt and van Horck1996), each of which may or may not be empty.Footnote ¹¹ In verb–complement constructs, the first member of the mother’s val is the xarg and the remaining members of the head daughter’s val are discharged from val as complement sisters. In subject–VP constructs, the singleton member of the head daughter’s val is the xarg and is discharged as a subject phrase. We will have to reformulate (38) in order to accommodate NI, however.

All information is uniformly represented in terms of typed feature structures, including phrasal structure. Thus, the tree on the left-hand side of Figure 1 is represented in terms of the feature structure on the right. The feature mtr singles out the mother node and the list-valued feature dtrs enumerates the immediate daughters of the construction. Constructs, but not signs, have the mtr and dtrs feature.

Figure 1 Phrasal constructs encoded as feature structures.

We will use the notation on the left when depicting structures licensed by the grammar. It is important to note, however, that the symbols “NP” and “VP” are merely abbreviations of feature structure descriptions. Thus, “NP” abbreviates any nominal sign (lexical or phrasal) with saturated (i.e. empty) valence, the reference of which has been determined by a binding quantifier (overtly or covertly).Footnote ¹² Similarly, “VP” abbreviates any verbal sign (lexical or phrasal) that still has not satisfied the requirement of combining with the external argument. This is shown in (39). Accordingly, “S” abbreviates a verbal sign with saturated valence, and so on.

1. (39)

   

   Linguistics 9Long description

   Two boxed feature structures with parts a and b, illustrating abbreviation conventions for N P subscript x and V P. Part a displays that N P subscript x abbreviates a structure of type sign. It contains S Y N field with three subfields as follows. C A T with value noun, V A L as an empty list in angle brackets, M A R K I N G with value det. S E M field containing I N D E X X in square brackets. Part b displays that V P abbreviates a structure of type sign. It contains S Y N field with C A T value verb, X A R G with value K. A V A L field with contents angle-bracketed K.

Constructs are defined as introducing exactly two features, mtr and dtrs, as shown in (40), from Sag (Reference Sag, Boas and Sag2012, 145). Furthermore, the value of the mtr feature is required to be of type sign, and the value of dtrs is required to be a non-empty list of signs (i.e. a feature structure of type n(on)-e(mpty)-list). In Section 3.2, we revise this constraint so that only overt signs are allowed in mtr and dtrs.Footnote ¹³

1. (40) Type declaration for construct [provisional]

   construct : $\left[\begin{array}{ll}\text{MTR}& \mathit{\text{sign}}\\ \text{DTRS}& \mathit{\text{ne}}\text{-}\mathit{\text{list}}(\mathit{\text{sign}})\end{array}\right]$

As in the case of lexeme types, there is a hierarchy of constructional types imposing constraints on the kinds of sign that that form constructs. In lexical constructions, the signs in dtrs are of type lexical-sign – that is, either lexeme or word – and in phrasal constructions they are of type expression – that is, either word or phrase.

The construction (41) from Sag (Reference Sag, Boas and Sag2012, 152) is responsible for allowing heads to combine with complements (the Predicational Head-Complement Construction; PHCC). The notation $X\varphi$, where $\varphi$ is an AVM, means that $\varphi$ contains exactly the same information as any AVM $\tau$ tagged as $X$: $\tau$ except information that is noted explicitly.Footnote ¹⁴ Because this is a headed construction (as indicated by the notation $\uparrow$headed-cxt), there is an additional feature hd-dtr that singles out which member of dtrs is the head sign. The operation “ $\oplus$” is the list concatenation relation, which is used to append lists.Footnote ¹⁵

1. (41)

   

   Linguistics 10Long description

   The boxed typed feature structure titled Predicational Head–Complement Construction with parenthetical headed-cxt and marked as provisional defines the pred-hd-comp-cxt construction as mapping to a complex structure. The structure contains three main fields. M T R contains a nested syntax field S Y N X subscript 1 with V A L list containing Y. D T R S is defined as the concatenation of angle-bracketed Z and L, a list labeled L colon ne-list. H D - D T R Z is labeled as word and contains a nested structure as follows. S Y N X subscript 1. Inside it, the C A T field contains X A R G with value Y. The V A L field contains the concatenation of angle-bracketed Y and L.

The constraint in (41) has the effect of requiring that the first daughter be a lexical head, and that all subsequent local sisters correspond to signs that are lexically subcategorized by the head. Thus, if the first member of dtrs bears a val(ence) specification like $⟨$ NP ${}_x$, NP ${}_y$, PP ${}_z⟩$ then $Y=$ NP ${}_x$ (the external argument), and $L=⟨$ NP ${}_y,$ PP ${}_z⟩$, licensing a VP like the one shown in Figure 2. Thus, whereas the head daughter is $[$val $⟨$ NP ${}_x,$ NP ${}_y,$ PP ${}_z⟩]$, the mother is specified as $[$val $⟨$ NP ${}_x⟩]$.

Figure 2 The VP contribute a lot to the cause (abbreviated).

Another example of a headed construction is shown in (42), which is responsible for combining an external argument with a verb phrase. Here, the second daughter is the head, which is required to be a finite, noninverted verb form, compatible with a nonauxiliary construction.Footnote ¹⁶ The result is a verbal sign that is fully saturated – that is, a clause.

1. (42)

   

   Linguistics 11Long description

   The boxed feature structure titled Subject–Predicate Construction with a parenthetical note headed-cxt represents the typed construction subj-pred-cxt, which maps to a feature structure with three main fields. The first field is M T R, which contains a syntax field S Y N X subscript 1 with an empty V A L list. The second field is D T R S, with values in angle brackets Y and Z. The third field is H D - D T R Z, with a nested structure: it contains S Y N X subscript 1 and a further nested C A T field with four subfields. These subfields are as follows. V F with value fin, I N V with value dash, A U X with value dash, X A R G with value Y. Below this, a V A L field contains a list with Y.

The Subject-Predicate Construction licenses structures like the one in Figure 3, where a subject NP is combined with its subcategorizing VP sister, to yield a clause.

Figure 3 The clause We contribute a lot to the cause (abbreviated).

Following Ginzburg and Sag (Reference Ginzburg and Sag2000, 45), we require the root node of a clause to be verbal, finite, and bear empty val and gap specifications, as specified in (43):

1. (43)

   

   Linguistics 12Long description

   The boxed feature structure expressing the structure of S subscript root defines it as a structure with a single main field labeled S Y N, which contains a nested set of attributes. Inside S Y N, there are three fields. The first is C A T, with value verb. Nested under C A T is V F with value fin, indicating a finite verb form. The second field is V A L, which contains empty angle brackets, representing an empty valence list. The third field is G A P, also with empty angle brackets, indicating no gap elements. The structure is enclosed in multiple layers of square brackets, displays hierarchical nesting.

Various other constraints come into play in SBCG, some of which are discussed later in this Element, as they have a more direct bearing on our analysis of NI. For our purposes, the present discussion suffices to illustrate the basic mechanics of the formalism and of the theory.

3.2 Lexically Licensed Null Instantiation

As discussed, lexically licensed null instantiation is optional and exhibits lexeme-specific patterns. The verb contribute allows the object to undergo INI and the PP to undergo DNI, and therefore have paradigmatic examples like (10), repeated here as (44).

1. 1. a. I will contribute ten dollars to your campaign.

   2. b. I will contribute _[something] to your campaign.

   3. c. I will contribute ten dollars _[to you know what].

   4. d. I will contribute _[something] _[to you know what].

In order to capture these facts explicitly, we assume that the NI potential associated with any given argument of a predicate is directly encoded in the argument structure of the corresponding lexeme. We further assume along with Pollard and Sag (Reference Pollard and Sag1994) that semantic indices are organized in a multiple-inheritance type hierarchy, forming a taxonomy of semantic indices, which we extend as shown in (45), in order to represent the optionality of NI perspicuously.

1. (45)

   

   Linguistics 13Long description

   The top node is labeled index and branches into two main types: canonical-index and non-canonical-index. Under canonical-index, there are two subtypes: referential-index and expletive-index. Expletive-index further branches into it-index and there-index. Under non-canonical-index, there are two subtypes: ni-index and pro-index. N i-index branches further into ini-index and dni-index.

According to this hierarchy, there are two major kinds of index: canonical and noncanonical. Canonical indices correspond to the expletive (semantically vacuous) indices introduced by the dummy pronouns it and there, as well as the semantically active indices occurring in overtly realized arguments. Noncanonical indices, on the other hand, can be of the NI variety, in which case they are interpreted contextually, without an explicitly overt correlate, or pro-indices, which are unexpressed in signs functioning as raised, controlled, or “arbitrarily” interpreted arguments. This organization of indices will play a key role in allowing us to use underspecification to constrain the NI potential of particular arguments.

We model indices via an index feature that includes an agreement feature (Pollard & Sag, Reference Pollard and Sag1994; Wechsler & Zlatic, Reference Wechsler and Zlatic2003) and a d(iscourse-)r(eferent) feature, as in Kamp and Reyle (Reference Kamp and Reyle1993) and Iordăchioaia and Richter (Reference Iordăchioaia and Richter2015). For example, the index information associated with the pronoun she is shown in (46). The types expletive-index are specified as [dr none], which automatically ensures that no expletive index can appear in the fes list. Since we use capital variables $X$... $Z$ for index values, lower case letters $x$... $z$ are reserved for the discourse referent variables.

1. (46)

   

   Linguistics 14Long description

   The boxed typed feature structure labeled (46). The outermost feature is INDEX, which contains three subfeatures arranged vertically. The first subfeature is labeled ref-index. The second is A G R, representing agreement, which contains a nested structure with three fields: P E R with the value 3 r d, N U M with the value sing, and G E N with the value fem. The third subfeature is D R with the value x, representing a discourse referent. Each field is enclosed within square brackets, and values are italicized.

We assume that semantic representations with free discourse referent variables are not interpretable, and therefore infelicitous. Hence, for a discourse referent variable to obtain a value it must either be explicitly assigned one via an equality (e.g. $x=robin$) or via a quantifier. The ni-index discourse referent variable are special in that they will be assigned values during interpretation, without the presence of a quantifier in the semantic representation (Farkas & de Swart, Reference Farkas and de Swart2003, ch. 3).Footnote ¹⁷ The interpretation of signs bearing ini-index or dni-index is discussed in Section 3.6. Next, we reformulate the sign type hierarchy in (30) slightly, as shown in (47), so that it becomes possible to distinguish between covert signs, which do not have any phonology or morphological form, and overt signs, which do. Thus, overt signs are morphophonologically potent lexemes, words, and phrases.Footnote ¹⁸

1. (47)

   

   Linguistics 15Long description

   At the top is the node labeled sign, which branches into overt-sign and covert-sign. From overt-sign, the structure continues downward into lexical-sign and expression. Lexical-sign further divides into lexeme and expression splits into word and phrase. The lexeme branch then continues downward into v-lxm, which stands for verb lexeme. From v-lxm, three branches appear: intrv-lxm, ptv-lxm, and drlv-lxm, representing intransitive, participial, and derived verb lexemes, respectively. Additional ellipses indicate further branches not shown.

We formalize the differing constraints on overt and covert signs in (48) by stating that the type sign introduces morphosyntactic, semantic, and pragmatic features, and that the type overt-sign in addition introduces morphophonological features. In other words, any feature structure of type overt-sign comes with phon and form information; it also comes with syn, sem, and cntxt information, via inheritance from the type sign.

1. (48)

   

   Linguistics 16Long description

   The boxed diagram has two subparts, a and b, presenting typed feature structures used in linguistics. Part a is labeled sign and contains three vertically stacked fields: S Y N with value syn-object, S E M with value linguistic-meaning, and C N T X T with value context-object. Part b is labeled overt-sign and contains two vertically stacked fields: P H O N with value phon-object, and F O R M with value morph-object. Each feature structure uses square brackets to enclose its fields, and each feature is written in spaced uppercase letters followed by a colon and its corresponding value in italicized text.

Thus, overt signs have the full set of features introduced in Sag (Reference Sag, Boas and Sag2012, 180), since they carry morphosyntactic information including the form and phonology.Footnote ¹⁹ Covert signs, on the other hand, do not carry the features form and phonology.

The conditional constraints in (49) specify that overt signs are required to have canonical indices (i.e. an expletive-index or a referential-index), and covert signs are required to have noncanonical indices (i.e. a dni-index, ini-index or pro-index).

1. 1. a. overt-sign $\Rightarrow$ [sem [index canonical-index ]]

   2. b. covert-sign $\Rightarrow$ [sem [index noncanonical-index ]]

Something must require the daughters of syntactic phrasal constructions in SBCG to be typed as overt-sign, preventing covert signs of any kind from appearing in syntax as silent phrasal nodes. To this end, we reformulate in (50) Sag’s (Reference Sag, Boas and Sag2012, 106) type constraint over constructs shown in (40). This type declaration ensures that all overt phrases in English are canonical – that is, either referential, it, or there.

1. (50) Type declaration for construct

   construct : $\left[\begin{array}{ll}\text{MTR}& \mathit{\text{overt}}\text{-}\mathit{\text{sign}}\\ \text{DTRS}& \mathit{\text{ne}}\text{-}\mathit{\text{list}}(\mathit{\text{overt}}\text{-}\mathit{\text{sign}})\end{array}\right]$

Finally, recall that the ARP in (38) is the constraint responsible for mapping arg-st specifications to val and gap. Whereas the val feature lists in situ arguments of a predicate (e.g. subjects and objects in their usual locations), the gap feature lists the ex situ arguments (e.g. topicalized, relativized, and interrogative arguments). We reformulate the constraint in (38) as shown in (51). The arg-st list is nondeterministically split into three sublists using the sequence union relation “ $◯$” (Kathol, Reference Kathol, Culicover and Postal2001; Reape, Reference Reape, Bunt and van Horck1996), each of which may or may not be empty. One sublist of arguments corresponds to val (i.e. locally realized arguments), another sublist corresponds to gap (i.e. extracted arguments), and a third sublist that must consist exclusively of covert signs (signs that will not be overt).

1. (51)

   

   Linguistics 17Long description

   The revised version of the Argument Realization Principle Construction defines a lexical-sign construction. The outer structure contains a word mapping to a boxed structure with two main components: A R G-S T and S Y N. The A R G-S T component consists of L subscript 1, followed by a small circle, L subscript 2, another small circle, and list of covert-sign. The S Y N component contains a nested structure as follows. Under V A L, it displays L subscript 1. Under G A P, it displays L subscript 2.

Although pro-index and ni-index signs can appear in val(ence) and gap, they cannot be discharged from those lists as per the definition of construct in (50), as only overt signs can appear in dtrs. Allowing pro-index signs in val allows us to license cases where an implicit argument is controlled by a predicator, and allowing such signs in gap allows us to displace such arguments.Footnote ²⁰ More specifically, the occurrence of a sign typed covert-sign with index pro-index in val licenses cases where a valent is controlled, as in the case of the subject valent of the VP go into a cup in (52a), or the relativized valent in (52b). In these cases, the implicit argument and its overt counterpart sign are required to have the same discourse referent $x$. Similarly, the occurrence of a covert-sign argument with index pro-index in the third sublist of arg-sg licenses understood imperative subjects, like (52c), for example. As already discussed in Section 2.3, these phenomena can co-occur, as in (52d). Null instantiation signs may appear only in the third sublist of arg-st, since (i) the definition of construct (50) requires all daughters to be overt signs and (ii) NI signs are by definition not controlled.

1. 1. a. I [made [the top]${}_x$ [${\mathrm{\varnothing }}_x$ go into a cup]].

   2. b. This is the top ${}_x$ [that [${\mathrm{\varnothing }}_x$ was damaged]].

   3. c. $\mathrm{\varnothing }$ Go to the last page.

   4. d. Don’t ${\mathrm{\varnothing }}_i$ be so hard to please _ ${}_i$.

      (Huddleston & Pullum, Reference Huddleston and Pullum2002, 1086)

The discourse referent variables of pro-index signs are unbound, and therefore not interpretable, but certain constructions, such as those in (52), bind the variables of pro-index arguments and allow them to be interpreted. The argument structure of a verb like contribute, specified as $⟨$ NP ${}_{x:\mathrm{\neg }ni-index}$, NP ${}_{y:\mathrm{\neg }dni-index}$, PP ${}_{z:\mathrm{\neg }ini-index}$ $⟩$, is consequently compatible with a total of 18 fully specified argument structures. For example, the subject can be resolved as ref-index (the subject is overtly realized) or pro-index (e.g. the subject is not realized, and is licit in controlled, imperative, or bare relative subject environments). Similarly the direct object can be resolved as ref-index, pro-index, or ini-index, and the oblique complement can be resolved as ref-index, pro-index, or dni-index. Any member of arg-st can be resolved a pro-index, since any argument can be relativized and extracted. See Section 3.5 for more details about extraction of implicit arguments in bare relative clauses.

Item (53) is an illustrative lexical entry (listeme) for contribute that resolves to just the possibilities just discussed. We assume that frame arguments appear as the value of the list feature fes, instead of the usual features (e.g. a situation (event variable) feature, and constituent features donor, gift, and recipient). This list encoding is chosen mainly as a convenient way to represent the linkage between arg-st members and the NI rules to be described later in this Element, though nothing hinges on this particular notational decision.Footnote ²¹

1. (53)

   

   Linguistics 18Long description

   The entry specifies its F O R M as contribute. Under the I N D E X attribute, it is associated with the variable S. The S E Mantics section includes a F R A M E S feature, which introduces a frame named contribute-fr. This frame contains a S I Tuation feature, which specifies that S is a reference index (r e f dash i n d e x) with a discourse referent (D R) labeled s. It also contains a F E S (Frame Element Structure) list that identifies three arguments or participants in the frame. The first is X, which is marked as having a non-initial index (n i dash i n d e x) with discourse referent x. The second is Y, which has a definite non-initial index (d n i dash i n d e x) and discourse referent y. The third is Z, labeled with an indefinite non-initial index (i n i dash i n d e x) and discourse referent z. Together, these attributes define the semantic and syntactic behavior of the verb contribute in this lexical entry.

Thus, the contribute-fr(ame) is encoded as in predicate logic, as contribute ($s,x,y,z$), where $s$ is a situation, $x$ is the donor, $y$ is the gift, and $z$ is the recipient, respectively. None of these arguments can have expletive indices, since such indices bear no dr variables and are therefore uninterpretable. Since expletive indices are not felicitous members of fes, the subject constraint $\mathrm{\neg }$ni-index licenses either ref-index or pro-index; the direct object constraint $\mathrm{\neg }$dni-index licenses either ref-index, ini-index, or pro-index; and the indirect object constraint $\mathrm{\neg }$ini-index licences either ref-index, dni-index, or pro-index.Footnote ²²

Recall that the hierarchical lexicon is responsible for instantiating arg-st values in lexemes and for binding the indices in frames to the appropriate arguments, as in (32), repeated here as (54), for prepositional transitive verbal lexemes like contribute in (53).

1. (54)

   

   Linguistics 19Long description

   The lexical entry for a predicate lexeme, abbreviated as p t v - l x m. It defines a feature structure with two major attributes. The first is A R G - S T, which lists three arguments: an N P with index X, an N P with index Y, and a P P with index Z. The second attribute is S E M, which contains a F R A M E S attribute. Within F R A M E S, there is an F E S list that includes the roles X, Y, and Z grouped together in angle brackets.

Thus, the effect of the constraint in (54) is to instantiate the value of arg-st of all verbal lexemes that correspond to prepositional transitive verbs, or more techically, to resolve the underspecified value of arg-st for all lexemes typed as instances of ptv-lxm. In the case of the contribute-lxm sign in (53), this results in the lexeme shown in (55). The values of dr are made explicit here for exposition purposes. The result is a lexeme that selects a subject NP that must be overtly realized, a direct object that can be overt or INI, and an oblique object that can be overt or DNI.

1. (55)

   

   Linguistics 20Long description

   The feature structure titled contribute-lxm. Under F O R M, the value is contribute. The I N D E X attribute is S. Under S E M, the F R A M E S attribute contains a contribute-fr frame, which includes situation S and discourse referent s. The nested F E S structure lists three semantic roles: X with N I dash index and discourse referent x, Y with D N I dash index and discourse referent y, and Z with I N I dash index and discourse referent z. The A R G dash S T attribute includes a noun phrase with index X, a noun phrase with index Y, and a prepositional phrase with index Z.

Suppose that $X$ resolves as ref-index, $Y$ as ini-index, and $Z$ as dni-index, and the lexeme undergoes past tense inflection. Then, the resulting word sign interacts with the ARP in (51) to make possible uses like (56a), by licensing signs like (56b). The subject NP I combines with the verb via the Subject-Predicate Construction in (42), and yields the clause (56b).

1. (56)

   

   Linguistics 21Long description

   Two parts. Part a displays the sentence: I contributed null null. Didn’t you? Part b presents a feature structure for the word contributed. Under F O R M, the value is contributed. The C A T attribute is verb, with X A R G as K and L I D as L. The V A L attribute includes the list K, and G A P is an empty list. The I N D E X is S. Under S E M, the F R A M E S attribute is labeled C O N T R I B U T E dash F R with situation S and discourse referent s. The nested F E S structure contains three referents: X with reference index and discourse referent x, Y with initial index and discourse referent y, and Z with D N I dash index and discourse referent z. Additionally, a P A S T dash F R frame is included with situation S. The A R G dash S T attribute includes K with noun phrase of index X, another noun phrase of index Y, and a prepositional phrase with index Z.

A derivation is shown in Figure 4, including the unary-branching step that inflects the verbal lexeme into the past tense word. The feature frames is omitted for perspicuity.

Figure 4 The clause I contributed.

If the subject is instead resolved as pro-index, it cannot then be discharged from val, because only canonical signs can appear in the feature dtrs. However, a controller verb (or other predicating word) can select a VP with a pro-index subject and bind its discourse referent to that of its complement, as in (57). Although only dr values are bound, rather than index values, we say that the two signs are co-indexed, in the traditional sense.

1. (57)

   

   Linguistics 22Long description

   Two parts. Part (a) contains the sentence I (square brackets) made him subscript x (second square bracket) subscript x contribute null null. Part (b) presents a feature structure labeled M A K E - L X M with the F O R M attribute set to make. The I N D E X is S. The S E M attribute includes a F R A M E S structure labeled M A K E - F R with a situation S and a discourse referent s. Inside F R A M E S is an F E S block containing X with n i - index and discourse referent x, Y with reference index and discourse referent y, and Z with reference index and discourse referent z. The A R G - S T attribute lists three arguments: a noun phrase with index X, a noun phrase with index Y and discourse referent y, and a verbal phrase with V P base. This V P has a V A L attribute including a noun phrase with pro - index and I N D E X Z, which shares the discourse referent y.

The verb make (“cause”) selects a subject, a direct object, and a base form VP. The unsaturated argument of the VP is pro-index and therefore has no phon or form information, as a covert-sign. The discourse referent (dr) $y$ of the unsaturated subject of the complement VP, however, is identified with make’s direct objects. The sentence in (57a) obtains the analysis in Figure 5, where made selects a direct object and binds its discourse referent $y$ to that of the unsaturated valent of the VP contribute.

Figure 5 The clause I made him contribute.

For resolutions where the direct object and/or the oblique object of contribute are resolved as bearing ref-index indices the result is essentially the same as above, except that now val is no longer a singleton list containing just the subject. Any complements resolved as ref-index are required by the ARP to appear in val (or gap, as detailed in Section 3.5). In (58), both the subject and the direct object are referential and the oblique complement is resolved as DNI.

1. 1. a. I contributed something θ. Didn’t you?

   2. b.

      

      Linguistics 23Long description

      There are 2 parts. Part (a) is a sentence that reads I contributed something null. Didn’t you? Part (b) displays a feature structure for the word contributed. The structure includes attributes such as F O R M, C A T, S Y N, V A L, G A P, I N D E X, S E M, and A R G - S T. Under F O R M, the value is “contributed.” C A T is of type verb and contains X A R G indexed with K and L I D indexed with L. V A L contains the elements K and W, and G A P is marked as empty. The I N D E X S substructure holds a reference index with discourse referent s. Under S E M, the F R A M E S attribute includes the frame “contribute - fr” labeled with situation S. Within F R A M E S is a nested F E S structure containing X, Y, and Z with respective reference indices and discourse referents x, y, and z. Z is also linked to d n i - index. The frame is further associated with past - fr and the same situation S. Finally, the A R G - S T lists three arguments: K as a noun phrase with index X, W as a noun phrase with index Y, and a prepositional phrase with index Z.

The complex VP contributed something is licensed by the application of the Predicational Head-Complement Construction in (41), discharging the complement NP $W$ as a rightward sister of the verb. The remainder of the clause is licensed in the usual way, via the Subject-Predicate Construction in (42), which discharges the subject NP $K$ from the VP’s val list, as usual. The result is depicted in Figure 6.

Figure 6 The clause I contributed something.

In so-called arbitrary-pro constructions like (59), we assume that the xarg of the lexical verb (err) is resolved as pro-index and that a generic quantifier is added to the frames list of that verb, binding the variable of the pro-index subject. All else proceeds as usual, according to independent principles. That is, the infinitive verb to selects a nonfinite VP complement and raises its subject as usual via the same structure-sharing mechanism already illustrated in Figure 5.

1. (59) $\mathrm{\varnothing }$ To err is human.

3.3 NI Licensed by Context

We now turn to cases where features of the discourse context, including narrative context and shared background knowledge, allow a predicator to exhibit NI potential it does not possess inherently. As discussed, in a situation of sufficient immediacy and salience, an object that does not inherently license DNI may remain implicit. Attested examples of Accessibility DNI were given in (13), and a subset are reintroduced here as (60).

1. 1. a. I leaped to my feet and stumbled toward her. My fingers grabbed for the deadly necklace. I pulled $\mathrm{\varnothing }$ with all my strength. Snap! (Stine, Reference Stineundated)

   2. b. Suddenly the boulder was rocking and Tola Beg pushed $\mathrm{\varnothing }$ hard, pushed $\mathrm{\varnothing }$ with all the strength he had in his old body and with all the strength he had in his mind. (L’Amour, Reference L’Amour2001, 36)

   3. c. ${}^{@}$ Announcer: And he’s behind Lehtonen, 3 seconds left, $\mathrm{\varnothing }$ passes it to Sutton, and THE THRASHERS WIN 2–0.

We take the key concept at work in licensing this kind of NI to be the accessibility of an intended referent (Ariel, Reference Ariel, Sanders, Schilperoord and Spooren2001; Gregory & Michaelis, Reference Gregory and Michaelis2001). As the name suggests, accessibility is conceived as a gradient property: the degree to which “the speaker can predict or could have predicted that a particular linguistic item will or would occur in a particular position within a sentence” (Prince, Reference Prince1981a, 226). We posit that in any utterance context there is a threshold degree $d$ of accessibility such that when the degree of accessibility of a referent $x$ denoted by a valent $v$ equals or exceeds $d$, DNI is licensed for $v$. The accessible feature is therefore discrete: A referent is accessible iff its degree of accessibility equals or exceeds the threshold.Footnote ²³ The accessible feature is posited to be one of the c(ontextual) features (see Sag (Reference Sag, Boas and Sag2012, 96) and Pollard and Sag (Reference Pollard and Sag1994, 332–335) for discussion of c-inds).

The Accessibility DNI Construction is a derivational construction (mapping lexemes to other lexemes) that allows a valent with a sufficiently accessible referent in the context to be interpreted as DNI. Thus, the construction a lexeme and outputs an otherwise identical lexeme in which the accessible valent is interpreted as DNI. The Accessibility DNI Construction is formalized in (61). The paired tags $X$ and $X!$ notate the fact that the values of mtr and dtrs are the same in all respects other than those that are explicitly shown to differ, as discussed in connection with (41).Footnote ²⁴ Thus, mtr and dtr have the same values for form and syn, and differ only relative to sem: One of the semantic arguments, $Y$, typed as ref-index in dtr, is now typed as dni-index in the mother node. Its dr variable remains the same $x$, nonetheless.

1. (61)

   

   Linguistics 24Long description

   The feature structure indicates a derivational context labeled as accessible d n c x t. The structure contains two main components: M T R indexed with X and D T R S indexed with X prime. Under M T R, the S E M attribute maps to F R A M E S, which contains a F E S structure that includes Y associated with d n i - index and additional layered information labeled L subscript 1 and L subscript 2, combined using the direct sum symbol. Also within M T R is a C N T X T attribute set to A C C E S S I B L E x. The D T R S component contains a S E M attribute that also maps to F R A M E S and includes a F E S structure with Y associated with ref - index. A D R x attribute is also present, followed by the same layered structure with L subscript 1 and L subscript 2 combined.

The accessible feature normally takes the value none, but in this construction it is required to take a variable of one of the referential arguments, indicating the accessibility of the intended referent $x$ is at or above threshold. The first frame in frames is the main predication (the root of the embedding tree of frames discussed in the text introducing the lid in [35]), so this is the only frame that needs to be altered by (61). As indicated by the ellipses ..., any such other frames remain unaltered by our NI lexical rules.

Recall that arg-st constraints like (54) apply to lexemes, which means that they apply to both the daughter and the mother of (61). Thus, the value of arg-st of the mother node is resolved as a list of valents, the indices of which are bound to the respective frame elements in fes. Thus, on the daughter’s arg-st list the accessible sign will have a ref-index, while on the mother’s arg-st list this otherwise identical sign has a dni-index. Both signs have the same [dr $x$] specification, since only the index type is altered by (61). An application of a construct licensed by (61) is illustrated in Figure 7, in tree format. The daughter node of Figure 7 corresponds to the sign in dtrs in (61) and the mother node is a sign that corresponds to the value of mtr.

Figure 7 Accessibility DNI construction applied to the internal argument of the verb pull.

Although the object of pull is listemically typed as ref-index, and therefore unable to be null instantiated, the construction in (61) can override this provided that its referent $x$ is deemed accessible in the given context.Footnote ²⁵ The general constraint for the arg-st of simple transitive verbs, shown in (62), ensures the arg-st value is properly instantiated, for both uses of pull seen in Figure 7.

1. (62)

   

   Linguistics 25Long description

   The linguistic feature structure rule for S T V - L X M. The rule maps A R G - S T to a list containing X P indexed with X and N P indexed with Y. Below it, the S E M attribute maps to F R A M E S, which contains a set with a feature structure F E S holding the pair ⟨X, Y⟩ and possibly other elements indicated by an ellipsis. The structure is enclosed in square brackets and angle brackets, formatted in a two-line attribute-value matrix.

We now turn our attention to dispositional NI. As already noted, Ruppenhofer and Michaelis (Reference Ruppenhofer and Michaelis2010) point out that generic, including habitual, aspect can license indefinite null instantiation of the direct object of a simple transitive verb, such as arrest, while this is not possible under other circumstances, as illustrated in (15), repeated here as (63) for convenience. See also Mittwoch (Reference Mittwoch, Erteschik-Shir and Rapoport2005) for related discussion.

1. 1. a. * The cops arrested $\mathrm{\varnothing }$ last night.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 159)

   2. b. Sure, the cops arrest $\mathrm{\varnothing }$ when they can, but it’s always in small amounts.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 159)

Even a strongly anti-NI verb like devour will allow object INI in dispositional contexts:

1. (64) Once Ragnarök is triggered, it will devour $\mathrm{\varnothing }$ until it has destroyed the last of this world. (Flowers, Reference Flowers2018)

Boneh (Reference Boneh2019) proposes a stativizing dispositional operator that may yield habitual, generic, or disposition readings depending on circumstances. Null complementation licensing habitual interpretation as exemplified above is restricted to a non-quantificational existence interpretation, INI (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 164), and is also restricted to non-subjects. We model these facts in the dispositional INI construction, shown in (65).

1. (65)

   

   Linguistics 26Long description

   The boxed diagram labeled (65) titled Dispositional I N I Construction, with superscript open parenthesis upward arrow end superscript derivational - c x t. It defines the dispositional - i n i - c x t construction using Attribute-Value Matrix (A V M) notation. The structure contains two main components: M T R X subscript 1 and D T R S angle bracket X angle bracket. Under M T R X subscript 1, the S E M attribute maps to F R A M E S, which includes F E S L subscript 1, combined using the spelled-out operator circle plus with L subscript 2, and contains the feature i n i dash index. This entire structure is paired with S I T S, labeled as dispositional dash f r, and then combined with L subscript 3 using circle plus. Under D T R S angle bracket X angle bracket, there is a nested structure where S E M maps to an inner A V M with I N D E X S and F R A M E S. Within F R A M E S, F E S L subscript 1 colon n e dash list, combined using circle plus with ref dash index and L subscript 2, is then combined with L subscript 3 using circle plus.

In (65), a nonsubject argument typed as ref-index is selected to become ini-index, regardless of the initial lexemic specification. We can ensure that the argument in question is not a subject because we assume that frame elements appear in order, in all English verbal listemes, such that the first frame element always corresponds to the external argument. The constraint [fes $L_1$:ne-list $\oplus ⟨$ ref-index $⟩\oplus L_2$], states that the list value of fes of the verb frame is split into three sublists: one non-empty $L_1$ sublist (which contains the referent of the subject), a singleton sublist containing a ref-index frame element, and a third sublist $L_2$ (which may or not be empty). As before, the value of arg-st of the mother node is underspecified and resolved via the linking rules that are appropriate given the lexeme type that is fed into the rule. As a result, a referential index is turned into a INI index, but its dr variable remains the same.

The change to a ini-index index, which is a noncanonical index, forces the sign bearing it to become covert-sign, according to (49). The mother’s frames list contains a dispositional-fr(ame), representing a stativizing operator that takes an event argument and subsumes a quasi-universal operator over instances of a kind (Boneh, Reference Boneh2019). The analysis is shown in Figure 8. We from now on omit the syn values from the derivation examples for exposition purposes, as they remain unchanged by NI constructions.

Figure 8 Dispositional INI construction as applied to the verb arrest.

Sentences like those in (66) have the look of counterexamples to the Boneh formulation of disposition, since they refer to a single episode. We note, however, that in each case a disposition to kill is presupposed or entailed. Dispositional INI is apparently sensitive to dispositions involved in an utterance that need not be asserted.

1. 1. a. ${}^{@}$ Once a bear has killed, it automatically earns the death penalty, as bears are creatures of habit and will get in trouble with humans again.

   2. b. ${}^{@}$ Once a dog has killed there is no going back, there’s no “training” for this, she’s tasted blood.

   3. c. ${}^{@}$ Once a dog has killed it is likely to kill again ...

   4. d. ${}^{@}$ I think it harks back to the old beliefs like once a dog has killed it will seek to do it again and again – the bloodlust theory.

3.4 NI Licensed by Genre

As already noted, Ruppenhofer and Michaelis (Reference Ruppenhofer and Michaelis2010) show there are at least five distinct genres that license NI: instructional imperative, “labelese,” diary style, sports reporting (“match reports”), and certain nonquotative verbs used quotatively. See Ruppenhofer and Michaelis (Reference Ruppenhofer and Michaelis2010, 160) for examples. Two examples of context-induced DNI illustrate what Ruppenhofer and Michaelis (Reference Ruppenhofer and Michaelis2010) term labelese – for example, (67a), and the diary genre – for example, (67b). For all five genres NI is of the deictic/anaphoric – that is, DNI, variety and, in some cases, targets erstwhile subjects.

1. 1. a. $\mathrm{\varnothing }$ Contains alcohol.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 160)

   2. b. $\mathrm{\varnothing }$ Read Michelet; $\mathrm{\varnothing }$ wrote to Desmond about his poetess; ... $\mathrm{\varnothing }$ played gramophone...

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 160)

Ruppenhofer and Michaelis (Reference Ruppenhofer and Michaelis2010) note that diary genre DNI involves the definite interpretation of an unrealized first-person subject that is necessarily a topic, and propose a phrasal construction for diary genre DNI to license examples like those in (18). Here, we remain with the lexical approach, as shown in (68), and view the accessibility of the author as entailed by the genre itself.

1. (68)

   

   Linguistics 27Long description

   The boxed diagram titled Diary Genre D N I Construction, with superscript open parenthesis upward arrow end superscript derivational - c x t. It defines the diary- d n i - c x t construction using Attribute-Value Matrix (A V M) notation. The top-level structure contains three main attributes: M T R X subscript 1, C N T X T, and D T R S angle bracket X angle bracket. Under M T R X subscript 1, the S E M attribute maps to F R A M E S, which contains F E S with feature d n i dash index, combined using the spelled-out operator circle plus with L subscript 1, followed by an ellipsis. Under C N T X T, the C dash I N D S attribute contains a nested A V M with T O P I C x and G E N R E diary. Under D T R S angle bracket X angle bracket, there is a nested A V M with S E M and F R A M E S. Within F R A M E S, F E S contains ref dash index and a nested attribute A G R, which includes P E R first, N U M singular, and D R x. This structure is combined using the spelled-out operator circle plus with L subscript 1, followed by an ellipsis.

In construction (68), the cntxt value constrains topic and genre features. The genre value is diary and the topic value is identified with the subject referent $x$. The mother’s value differs from that of the daughter in that the subject’s index is ref-index in the daughter and dni-index in the mother, as in Figure 9. The frame element typed dni-index in mtr retains all the information it has in dtrs, including agr and dr.

Figure 9 Diary genre DNI construction as applied to the verb read.

The labelese genre consists of structures describing generic properties of provenance and purpose of the item in question, as illustrated in (67a) and (69).

1. 1. a. $\mathrm{\varnothing }$ Processed in a facility that processes tree nuts.

   2. b. $\mathrm{\varnothing }$ Manufactured using equipment that processes shellfish.

   3. c. $\mathrm{\varnothing }$ Gives long-lasting shine $\mathrm{\varnothing }$.

Our account of the labelese construction is very similar to that of the diary genre, as seen in (70). A referential subject is recast as DNI and the construction is only appropriate in a particular kind of context. Further constraints on frames are necessary, requiring that $x$ denote a (manufactured or agricultural) product with a given purpose. This could be effected by appending $product(x)$ to the value of frames in the mother node of (70).

1. (70)

   

   Linguistics 28Long description

   The boxed diagram titled Labelese Genre D N I Construction, with superscript open parenthesis upward arrow end superscript derivational-cxt defines the labelese-dni-cxt construction using Attribute-Value Matrix (A V M) notation. The top-level structure contains three main attributes: M T R X subscript 1, C N T X T, and D T R S angle bracket X angle bracket. Under M T R X subscript 1, the S E M attribute maps to F R A M E S, which contains F E S with feature d n i dash index, combined using the spelled-out operator circle plus with L subscript 1, followed by an ellipsis. Under C N T X T, the C dash I N D S attribute includes a nested A V M with T O P I C x and G E N R E labels. Under D T R S angle bracket X angle bracket, there is a nested A V M containing S E M and F R A M E S, where F R A M E S contains F E S with ref dash index and D R x, combined using the spelled-out operator circle plus with L subscript 1, followed by an ellipsis.

We now turn our attention to instructional imperatives, but in order to do so, we need to settle on an account of imperative constructions. As is well known, imperative constructions allow the omission of a second-person subject, as an implicit addressee, which is assigned the same semantic content for the understood subject as the pronoun you. Sag et al. (Reference Sag, Wasow and Bender2003) propose to account for imperatives with a (nonheaded) phrasal rule that projects a finite S node from a nonfinite VP daughter. Such a rule is nonheaded because the verb form feature (encoded as a head feature) of the daughter is inconsistent with that of the mother. But this difference suggests instead that the imperative should be a derivational lexical rule. We therefore assume that imperatives are obtained via a derivational rule whose daughter is a base form lexeme and whose mother is a morphologically a plain-form (Huddleston and Pullum Reference Huddleston and Pullum2002, 83, [CGEL]) verb, whose xarg appears on neither the val nor gap lists and is interpreted like a second-person pronoun, as formalized in (71).

1. (71)

   

   Linguistics 29Long description

   The diagram represents the Imperative Construction, referred to as imperative dash c x t. The structure is vertically bracketed and divided into M T R and D T R S fields, each containing multiple nested specifications. The M T R field labeled X subscript 1 includes the syntactic category with V F O R M set to plain. The semantic field includes F R A M E S, which combines F with imper dash f r, which contains S I T S and F E S with set Y in angled brackets. The context field C N T X T includes C dash I N D S with addressee y. The D T R S field is labeled as X subscript 2 and also contains syntactic category with V F O R M plain. The semantic field includes I N D E X S and F R A M E S F. The A R G dash S T field is marked as covert and contains a semantic index Y. This is linked to a pro dash index structure indicating agreement features A G R with person P E R specified as second and discourse referent y.

In (71), the subject is required to be resolved as a covert pro-index sign. Such a resolution was a possibility all along, since external arguments in listemes generally have the pro-index option and do not cause a problem so long as they are given an interpretation, for example, in control environments, as already discussed. The definition of construct in (50) prevents the subject from being realized overtly because of its index type, but it remains available on the arg-st to bind an anaphor if necessary, as in (72).Footnote ²⁶

1. (72) ${\mathrm{\varnothing }}_x$ Protect yourself ${}_x$ from 5G.

We assume imperative semantics consists in a relation between an individual $Y$ (the understood second person subject) and a state of affairs $\mathit{\text{S}}$, as indicated in the mother’s frames in (71). Other possibilities exist. The application of the rule in (71) is illustrated in Figure 10.

Figure 10 Derivation of the imperative form for protect in (72).

Recall that we define a root clause as any verbal sign with empty val and gap specifications, as seen in (43). The verbal lexemes licensed by the imperative construction can satisfy such a constraint because the ARP allows pro-index covert signs to be absent from val and gap. Thus, we get structures like the one in Figure 11.

Figure 11 The clause Protect yourself from 5G! (abbreviated).

We are now in a position to address the instructional imperative. This construction is of interest because, along with DNI suppression of a nonsubject argument, it includes the familiar unexpressed second-person subject of imperatives, as in (73).

1. 1. a. Method: Blend all the ingredients in an electric blender. Serve $\mathrm{\varnothing }$ cold.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 106)

   2. b. Chill $\mathrm{\varnothing }$ before serving $\mathrm{\varnothing }$.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer and Michaelis2010, 159)

   3. c. In a bowl, toss $\mathrm{\varnothing }$ with salt and set $\mathrm{\varnothing }$ aside.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer, Michaelis, Bourns and Myers2014, 72)

   4. d. In a skillet, sauté $\mathrm{\varnothing }$ until browned but not crisp.

      (Ruppenhofer & Michaelis, Reference Ruppenhofer, Michaelis, Bourns and Myers2014, 72)

Although Bender (Reference Bender, Alexander, Han and Fox1999) and Ruppenhofer and Michaelis (Reference Ruppenhofer and Michaelis2010) propose a phrasal construction, we continue here to pursue a lexical approach, treating these phenomena as licensed by derivational lexical constructions. We analyze the uses of the verbs verbs chill and serve in (73) via the instructional imperative construction, formalized in (74). Here, the daughter is an imperative verb lexeme – that is, the output (mtr) of the imperative construction in (71).

1. (74)

   

   Linguistics 30Long description

   The labeled diagram represents the Instructional Imperative D N I Construction, referenced as instructional dash imperative dash d n i dash c x t. The structure is organized into two main components: M T R and D T R S. In the M T R field, variable X subscript 1 has a semantic feature labeled F R A M E S, which contains an F E S value L subscript 1 combined with d n i dash index and then combined with L subscript 3. The D T R S field is labeled as X subscript 2 with type imper dash l x m. Its S E M field contains a nested F R A M E S structure with F E S L subscript 1 combined with r e f dash index. D R is set to x, and this is combined with L subscript 2 and then L subscript 3. A separate discourse context field C N T X T includes C dash I N D S with T O P I C x and G E N R E set to instruction.

The mtr in the instructional imperative construction retains the characteristics of an imperative verb word that contains a referential nonsubject argument while replacing the index of that argument with dni-index.

Specifically, in the instructional imperative construction (71); (i) there is a pair of non-xarg arg-st members distributed across mother and daughter that are alike in having [dr $x$] in their index but differ in their index type, (ii) in the daughter’s arg-st, the index type of the [dr $x$] argument is ref-index while that in the mother’s arg-st is dni-index, (iii) the $x$ variable is contextually specified to be a topic and (iv) the genre is contextually specified to be instruction(al). The analysis is illustrated in Figure 12.Footnote ²⁷

Figure 12 Instructional imperative DNI construction as applied to the verb chill.

3.5 Implicit Arguments and Displacement

Not all extraction requires a filler phrase, and thus in some cases the missing argument is simply missing, although it can be co-indexed with another implicit phrase. In examples (75a) and (75b), the reference of the implicit subject is constructionally controlled, and therefore best seen as pro.

1. 1. a. Don’t ${\mathrm{\varnothing }}_x$ be so hard to get _ ${}_x$, baby.

      [Rick James, You and I]

   2. b. ${\mathrm{\varnothing }}_x$ Being especially easy to talk to _ ${}_x$, Pat ${}_x$ was set to become a great therapist.

In the case of (75a), the extracted theme is required to be the imperative subject (i.e. a second-person nominal who is the addressee), whereas in (75b), the dangling participle construction independently requires the external argument of the prepended phrase to be co-referential with the external argument of the matrix clause. This contrasts with NI, whereby context determines the reference of the implicit arguments rather than a controller introduced by the construction.

Sag (Reference Sag, Boas and Sag2012) adopts a feature-based approach to argument realization in which members of arg-st are allowed to appear either in val(ence) or in gap. Members of arg-st that appear in gap are percolated in syntactic structure to license potentially long-distance dependencies, whereas those members of arg-st that appear in val must be locally realized. However, Sag (Reference Sag, Boas and Sag2012) is not entirely clear about how members of arg-st are related to val and gap, in particular, how subjects are mapped into gap.Footnote ²⁸ Moreover, the PHCC in (41) forces the external argument to always be on the val list, which in turn incorrectly prevents subject extraction in VPs. We therefore revise the PHCC as seen in (76).

1. (76)

   

   Linguistics 31Long description

   The structure diagram describes the Predicational Head-Complement Construction, labeled pred dash h d dash comp dash c x t and marked as revised. The structure includes three main sections: M T R, D T R S, and H D dash D T R Z. The M T R field contains S Y N X with a V A L feature equal to L subscript 1. The D T R S field is a combination of Z and L subscript 2, denoted as n e dash list. The H D dash D T R Z field expands to a word with a nested S Y N X structure. Inside it, the C A T field includes X A R G Y, and the V A L field is composed of L subscript 1 with a singleton angled bracketed Y, combined with L subscript 2 as a list excluding Y.

Recall that the ARP in (51) allows any member of arg-st (including the xarg) to appear on either the val list or on the gap list. The version of the PHCC in (76) interacts with the ARP to allow any argument (including the external argument) to be overtly realized (locally or nonlocally). This is possible because the val list of the head daughter is the concatenation “ $\oplus$” of two sublists: $L_1$ and $L_2$. The first list $L_1$ must (at most) contain the xarg (the parenthesis around $Y$ in $⟨(Y)⟩$ express optionality), and the latter list $L_2$ is required to be non-empty and prohibited from containing the xarg (i.e. the parametric type list($\mathrm{\neg }Y$) states that none of the members of the list $L_2$ can unify with $Y$). Thus, if the xarg is in val, then that subject phrase is realized locally, and if instead the xarg appears on the gap list, then the phrase has been extracted.

We can now turn to the problem of modeling the interaction between displacement and implicit arguments. Our grammar predicts the acceptability of pro in missing object constructions such as (75), repeated as (77), without further stipulation.

1. 1. a. Don’t ${\mathrm{\varnothing }}_x$ be so hard to please _ ${}_x$.

      (Huddleston & Pullum, Reference Huddleston and Pullum2002, 1086)

   2. b. ${\mathrm{\varnothing }}_x$ Being especially easy to talk to _ ${}_x$, Pat was set to become a great therapist.

Signs that are of the sort pro-index are not allowed in dtrs because the definition of construct in (50) requires daughters to be overt signs, but they are allowed in gap. This predicts that the object of please in (77a) can be typed pro-index and appear in gap. The sign is percolated in the sentence structure like any other extracted sign, and is instantiated with the external argument of the adjective hard as in Figure 13.

Figure 13 Percolation of a gap into an understood external argument in a missing object construction.

The subject $X$ of the adjective is raised like any other subject all the way to the VP selected by the auxiliary verb. At this point, the dr of the remaining valent in the VP val list is instantiated with the external argument of the auxiliary. In this case, the verb is in imperative mood, and therefore its understood subject is also pro-index, as required by the imperative construction. The same analysis applies to (77b). In bare relatives like (78a) an analogous situation arises: the extracted pro argument is percolated via gap, and the construction itself links its dr to the head of the relative, binding it, via a general construction (approximately) of the form N ${}_x$ $\to$ N ${}_x$ S[gap $⟨$ NP ${}_x$[index pro-index]$⟩$]; see Sag (Reference Sag1997) and Sag (Reference Sag2010). Thus, although the implicit argument is a gap, the clause is licit because the sign is discharged from the gap list. The same applies to most non-wh-relative constructions, including for infinitival relatives like (78b), and to infinitival relatives like (78c).

1. 1. a. The book ${}_x$ [(that) I want you to read _ ${}_x$] is this one.

   2. b. Sam found a person ${}_x$ [for you to talk to _ ${}_x$].

   3. c. The next contestant ${}_x$ [_ ${}_x$ to answer the question correctly] will get bonus points.

Conversely, the present account predicts that examples like (79) are illicit. No type of covert sign is allowed in dtrs, and thus there is no way to discharge a covert sign in gap and saturate the root sign. Recall that all root signs must be verbal, finite, and bear empty val and gap specifications (Ginzburg & Sag, Reference Ginzburg and Sag2000, 45).

1. 1. a. *${\mathrm{\varnothing }}_x$ Do you think is easy to talk to _ ${}_x$?

      (cf. ‘Who ${}_x$ do you think is easy to talk to _ ${}_x$?’)

   2. b. *${\mathrm{\varnothing }}_x$ I don’t think I’ve met _ ${}_x$.

      (cf. ‘that guy${}_x$ I don’t think I’ve met _ ${}_x$.)

Let us now turn to the passivization of implicit arguments like (80). Such cases are likewise predicted without stipulations. In (80a), the NI direct object has been promoted to a passive subject. As usual, we assume that the lexical rule for passivization promotes the direct object to subject, and so the first member of arg-st of the passive form fed in (80a) is the ni-index theme. The example in (80b) has the extra complication that the passive subject is co-indexed with the prepositional object. The passive rule interacts with the grammar of missing object constructions to identify the extracted complement with the first member of arg-sg of take.

1. 1. a. If ${\mathrm{\varnothing }}_x$ properly fed _ ${}_x$, iguanas can live for a long time.

   2. b. If ${\mathrm{\varnothing }}_x$ taken good care of _ ${}_x$, iguanas can live for a long time.

Extant accounts of the passive such as Pollard and Sag (Reference Pollard and Sag1994, 83), Boeckx (Reference Boeckx1998), and Bresnan (Reference Bresnan2001, 26), offer no principled (semantic/pragmatic) account of the optionality of the PP. Usually, the by-phrase is simply assumed to be optional. In this Element, we seek to ground this optionality in the cognitive status of the demoted agent. There are clear cases of INI interpretation of short passives such as (81).

1. 1. a. ${}^{@}$ I heard that they had been killed $\mathrm{\varnothing }$, but no one knew who did it.

   2. b. Two of them were shot by the demonstrators and another person was killed $\mathrm{\varnothing }$, but no one knows by whom.

There are also cases like (82), which have suggested DNI to Fillmore and some later writers (see Lyngfeld (Reference Lyngfeld2012) for discussion and a third point of view). There appears to be an equally good case to be made for attributing the definite-seeming reading arising from cases like those in (82) to existential semantics strengthened by pragmatic inference. Guided by the principle of claiming no more for semantics per se than necessary, we model the semantics of short passive agents as INI.

1. 1. a. ${}^{@}$“Have those teeth been brushed this year $\mathrm{\varnothing }$?” Adella asked … “I know I brushed mine in April for my birthday!” quipped the younger …

   2. b. ${}^{@}$ Only after the gloves have been removed $\mathrm{\varnothing }$, the hands have been washed $\mathrm{\varnothing }$, the patient has been dismissed $\mathrm{\varnothing }$, and the area has been cleaned $\mathrm{\varnothing }$, should the dental radiographer carry the disposable container holding the contaminated films to the darkroom.

We propose to model both long and short passives with the lexical rule in (83). The daughter must subcategorize an overt subject argument and at least one object, $Y$. The passive counterpart must have the appropriate inflection, via the ancillary morphological function $f_{pass}$. In the mother node, the object $Y$ is now the subject, as it is the first element in arg-st. If the PP at the end of the arg-st is resolved as an overt sign, we obtain a long passive. If the PP is resolved as a covert sign, we obtain a short passive. Recall that covert signs are allowed in val in our ARP, but they cannot be discharged because only overt-signs can appear in dtrs.Footnote ²⁹

1. (83)

   

   Linguistics 32Long description

   The labeled feature structure diagram describes passive construction with the label passive dash c x t double arrow. The structure is enclosed in a large bracket divided into two main sections: M T R and D T R S. In the M T R section, the P H O N attribute is f subscript pass of L subscript 3. The S Y N attribute contains C A T with V F O R M as pass and X A R G as Y. The S E M attribute labeled Z includes F R A M E S with a set of features W combined with L subscript 2. The A R G dash S T field is Y combined with L subscript 1 and a P P phrase marked by the preposition by. This P P phrase contains an I N D E X field W subscript x and allows values i n i dash index or r e f dash index, with D R as x. In the D T R S section, P H O N is L subscript 3. S Y N includes C A T with V F O R M as base. S E M labeled Z includes F R A M E S with F E S containing X combined with L subscript 2. The A R G dash S T field refers to overt dash sign, indexing X and including a reference index and another argument list Y combined with L subscript 1.

The subject and xarg of the passive form of a transitive verb will be the second member of the daughter’s arg-st, here $Y$, as a consequence of the constraint in (45), which states that the first member of arg-st is structure-shared with xarg. The xarg variable $x$ is now linked to the PP argument. As usual, the ARP in (51) is responsible for resolving the values of val and gap, given the content of arg-st.

An example of a short passive is depicted in Figure 14. Here, the PP in arg-st is resolved as a covert-sign with a ini-index and therefore it is missing from val and gap. Had the PP been resolved as overt-sign, then its index would be ref-index and the PP would have been overtly realized as a complement of feed.Footnote ³⁰

Figure 14 Short passive clause It was fed (abbreviated).

Note that in our analysis, the implicit agent of the short passive is still a member of arg-st, which predicts that it should be visible to binding theory as in (84).

1. 1. a. ${}^{@}$ The first “email” was sent by Ray Tomlinson in 1971. He chose the @ sign to separate the local part from the domain. The first email address was “tomlinson@bbntenexa” and the email was sent to himself.

   2. b. ${}^{@}$ The very first email was sent by computer engineer Ray Tomlinson on July 1st 1971. The message probably consisted of only a few words and letters and was sent to himself, but the implications would change communications worldwide forever.

   3. c. ${}^{@}$ In a newly declassified email that Susan Rice sent to herself on January 20, 2017, the former national-security adviser said that … Rice’s email was sent to herself 15 days after the Oval Office meeting.

   4. d. ${}^{@}$(...) a settlement had been executed by Miss Bolton as soon as she came of age, by which an absolute general power of appointment was given to herself and her proposed husband jointly in priority to the other trustees of the settlement.

Our account also predicts that an implicit passive agent can control secondary predicates, as we noted in Section 2.3, with examples like (85a,b) or pro subjects of infinitives as in (85c). Lexically licensed NI – for example, of active-voice objects, can equally control secondary predicates, as in (85b). In our analysis, such NI arguments are still members of arg-st, and therefore are visible to the independently motivated valence-extending constructions that license such control structures.

1. 1. a. ${}^{@}$ The game was played barefoot.

   2. b. ${}^{@}$ The first football match the Nigerian football team played!! They played barefoot and won the match 5–0.

   3. c. The boat was sunk to collect the insurance.

      (Jackendoff, Reference Jackendoff1987, 408)

3.6 Semantics of NI

We now turn to how discourse referents associated with INI and DNI indices are interpreted. One possibility would be to add a definite quantifier to the semantic representation of DNI arguments and an indefinite to that of INI arguments, which could be done by modifying the constructions discussed so far, or via closure rules. However, we believe that adding quantifiers would make the wrong predictions. For example, if INI signs were bound by an existential quantifier, then such quantifier would be expected to give rise to scope ambiguities, all else being equal, but this prediction is not borne out.

Consider the examples in (86), which contain no implicit arguments. As expected, two readings of the indefinite NP “a check of $100” arise depending on whether it receives wide or narrow scope.

1. 1. a. I didn’t contribute a check ${}_x$ of $100 to the Red Cross. That ${}_x$ was a gift from someone else. I gave a 5 dollar bill.

      (Wide scope: $\mathrm{\exists }x(check(x,\mathrm{\$}100)\wedge \mathrm{\neg }contribute(I,x)))$

   2. b. I didn’t contribute a check ${}_x$ of $100 to the Red Cross. In fact, I’ve never made any contributions, ever.

      (Narrow scope: $\mathrm{\neg }\mathrm{\exists }x(check(x,\mathrm{\$}100)\wedge contribute(I,x)))$

However, only the narrow scope reading is possible if the theme is INI instead, as (87) illustrates, a an observation originally due to Condoravdi and Gawron (Reference Condoravdi, Gawron, Kanazawa, Piñón and de Swart1996, 3).

1. (87) I didn’t contribute $\mathrm{\varnothing }$ to the Red Cross.

   (= I didn’t contribute anything to the Red Cross)

Like its overt counterparts in (86), the INI theme is usually anaphorically accessible to discourse continuations, as in (88a). But as expected, such anaphora are not possible in the presence of negation precisely because the INI theme must reside under its scope, as (88b) shows.Footnote ³¹ Thus, the continuation in (88b) has no antecedent to bind to.

1. 1. a. I contributed ${\mathrm{\varnothing }}_x$ to the Red Cross. It ${}_x$ was a rather large sum.

   2. b. I didn’t contribute ${\mathrm{\varnothing }}_x$ to the Red Cross. #It ${}_x$ was a rather large sum.

Attested examples of NI anaphoric dependencies are provided in (89).

1. 1. a. The children began to sing ${\mathrm{\varnothing }}_x$. It ${}_x$ was the song Henryk Bley had composed with them before they went.

      [COCA 1990 FIC]

   2. b. ${}^{@}$[The] young lady reminded us they close at 4 so we ate ${\mathrm{\varnothing }}_x$ quickly and it ${}_x$ was good but a little overpriced.

   3. c. Thirteen said, “you gotta give people food, you know? I mean, to be peaceable.” Behind him, Smokey, plate just under her chin, ate ${\mathrm{\varnothing }}_x$ eagerly. It ${}_x$ had meat in it too. (Delany, Dhalgren, 138)

Incidentally, anaphora can target INI passive agents as well, as evidenced by (90). See Koenig and Mauner (Reference Koenig and Mauner1999, 216) and Mauner and Koenig (Reference Mauner and Koenig2000) for arguments that such dependencies are instances of bridging (Clark, Reference Clark1975; Erkü & Gundel, Reference Erkü, Gundel, Verschueren and Bertuccelli-Papi1987; Hawkins, Reference Hawkins1978; Prince, Reference Prince and Cole1981b).

1. 1. a. ${}^{@}$ The first time I was ghosted ${\mathrm{\varnothing }}_x$ he ${}_x$ came back 3 months later...

   2. b. ${}^{@}$ You won’t believe this but I have witnesses. When I was carjacked ${\mathrm{\varnothing }}_x$ he ${}_x$ hopped into my passenger seat and set the gun on his lap...

   3. c. ${}^{@}$ I’m so sorry that happened friend. When I was assaulted ${\mathrm{\varnothing }}_x$, he ${}_x$ drugged me first...

   4. d. ${}^{@}$ I got married ${\mathrm{\varnothing }}_x$, she ${}_x$ cheated on me, and she’s pregnant by someone else!

Given these observations, we conclude that NI arguments are not associated with any quantifier in logical form. In our account, the variables associated with indices typed ini-index are directly interpreted as existential indefinites, and variables associated with indices typed as dni-index are directly interpreted as definites. Following Farkas and de Swart (Reference Farkas and de Swart2003, ch. 3) we assume that such direct interpretations are enforced model-theoretically: When the semantic representation is interpreted against a model, the variables that are associated with ini-index and dni-index are interpreted as if they had a quantifier. The truth-conditional interpretation for $n$-ary predicate $P$ is traditionally formalized as $[[P(x_1,...,x_i)]]=1$ iff $⟨[[x_1]],...,[[x_n]]⟩\in F(P)$, where $F$ is the interpretation function. We adopt this approach to the interpretation of our semantic frames as seen in (91). By P-fr we mean a variable over frame predicate types.

1. (91)

   

   Linguistics 33Long description

   The labeled formula presents a boxed semantic representation. Double square brackets enclose P dash f r, which contains two fields: S I T with value S and F E S with values in angled brackets X subscript 1 through X subscript n. The formula is equated to 1 if and only if the tuple of denotations of S, X subscript 1 through X subscript n belongs to F of P dash f r.

The interpretation of ref-index and pro-index indices is straightforward: For all $X_{\mathrm{1..}n}$ indices, the value of their respective discourse markers is determined by the valuation function $val()$ as shown in (92).

1. (92)

   

   Linguistics 34Long description

   Two boxed semantic expressions labeled a and b. In part a, double square brackets enclose r e f dash index over D R and v, equated to v a l of v. In part b, double square brackets enclose p r o dash index over D R and v, also equated to v a l of v.

In order for $val(v)$ to be defined, the variable $v$ has to already have been bound to a quantifier or to an equality. Otherwise, $val(v)$ is undefined and the value of $v$ has no interpretation, as usual in certain semantic theories like Groenendijk and Stokhof (Reference Groenendijk and Stokhof1991), Kamp and Reyle (Reference Kamp and Reyle1993), and Kamp and van Eijck (Reference Kamp, van Eijck, van Benthem and ter Meulen1997). Thus, the discourse markers of ref-index and pro-index signs are free, and cannot be interpreted with $val()$. Farkas and de Swart (Reference Farkas and de Swart2003, ch. 3) propose to solve the problem of defining the truth-conditions of predicates with implicit arguments by allowing the denotation of the predicate to determine the value of its free variables. We do the same, but in addition introduce constraints that account for the differences between DNI and INI.

We augment (92) with two extra cases, drawing from Gundel, Hedberg, and Zacharski’s (Reference Gundel, Hedberg and Zacharski1993) implicational givenness hierarchy for NPs. We assume that an entity e that is the value of a DNI variable must be a uniquely identifiable member of the Dom(ain) in the given context, as shown in (93a). A uniquely identifiable referent is an entity that is in the set of given entities and that has core characteristics which are not shared by any other entity that is also given. This uniquely identifiable constraint is independently needed to license the use of definite descriptions (Gundel et al., Reference Gundel, Hedberg and Zacharski1993).

1. (93)

   

   Linguistics 35Long description

   Two semantic formulas labeled a and b. In part a, double square brackets enclose d n i dash index over D R and v, equated to e if and only if there exists an e such that e is an element of D o m and Uniquely Identifiable of e, and the value of v equals e. In part b, double square brackets enclose i n i dash index over D R and v, equated to e if and only if there exists an e such that e is an element of D o m and Type dash Identifiable of e, and the value of v equals e.

The variables of NI indices implicitly evoke a quantificational interpretation as in (93). Thus, for NI variables, their value is some entity from Dom.Footnote ³² In this analysis dni-index referents have uniquely identifying properties in the given context, just like those referents that are characterizable with the definite determiner the. Analogously, the entity $e$ in (92b) must be type-identifiable, rather than uniquely identifiable. Thus, ini-index referents are not assumed to be known by the addressee, just like those referents that are characterizable with indefinite determiner a(n).

As in Gundel et al.’s (Reference Gundel, Hedberg and Zacharski1993) account of definite and indefinite determiners, the interpretation of DNI and INI variables depends on their cognitive status, not logical form. The entity that is identified according to Gundel et al.’s concept of unique identifiability is without mystery; the Domain is a set of individuals and the entity identified is a member of that set. The concept of type identifiability is less straightforward. Although providing several helpful illustrative examples, the only abstract statement of the concept provided is “Type Identifiable: The addressee is able to access a representation of the type of object described by the expression” (Gundel et al., Reference Gundel, Hedberg and Zacharski1993, 276). We interpret the “type of object” notion set-theoretically as shown in (94).

1. (94) An individual i in domain Dom is type-identifiable in utterance u iff an auditor of u can ascertain in context a proper subset of Dom of which i is a member.

The construal of implicit arguments as prototypical participants, and their failure to behave like regular quantified arguments thus follows from their status. Once an NI variable is assigned a value by the $val()$ function, it may be anaphorically bound, as in (89). It has become salient in the speaker’s mental representation. See Farkas and de Swart (Reference Farkas and de Swart2003, ch. 3) for a unification-based mechanism for binding to implicit arguments that is fully compatible with the present account, and see also Condoravdi and Gawron (Reference Condoravdi, Gawron, Kanazawa, Piñón and de Swart1996) for a related analysis of the interpretation of implicit locative anaphora.