The formalization of semantics

By ‘logical semantics’ is here meant the study of meaning with the aid of mathematical logic. The term is commonly used by logicians in a narrower sense than this: to refer to the investigation of the meaning, or interpretation, of expressions in specially constructed logical systems. (The term ‘expression’ will be employed throughout this chapter in the sense in which it is customarily employed by logicians: cf. 1.5). Logical semantics in this narrower and more technical sense may be referred to, following Carnap (1942, 1956), as pure* semantics. It is a highly specialized branch of modern logic, which we shall be concerned with only in so far as it furnishes us with concepts and symbolic notation useful for the analysis of language. The present chapter is not therefore intended as an introduction to pure semantics; and it should not be treated as such by the reader. We will not discuss such questions as consistency and completeness; and no reference will be made to axiomatization or methods of proof.

Constructed logical systems are frequently referred to as languages. But we will not adopt this usage. We will refer to them, instead, as calculi*, keeping the term ‘language’ for natural languages. This will enable us to oppose linguistic semantics* (a branch of linguistics) to pure semantics* (a branch of logic or mathematics). Linguistic semantics, like other branches of linguistics, will have a theoretical and a descriptive section.

Signification

The meaning of linguistic expressions is commonly described in terms of the notion of signification*: that is to say, words and other expressions are held to be signs* which, in some sense, signify*, or stand for, other things. What these other things are, as we shall see, has long been a matter of controversy. It is convenient to have a neutral technical term for whatever it is that a sign stands for: and we will use the Latin term significatum*, as a number of authors have done, for this purpose.

Many writers, in discussing the notion of signification, have drawn a distinction between signs and symbols, or between signals and symbols, or between symbols and symptoms. Unfortunately, however, there is no consistency in the way in which various authors have defined these terms. For example, Ogden and Richards (1923: 23) distinguish symbols as “those signs which men use to communicate with one another”, whereas Peirce (1940: 104), who also treats symbols as a subclass of signs, defines them, as we shall see, on the basis of the conventional nature of the relation which holds between sign and significatum. So too does Miller (1951: 5). But Morris (1946: 23–7), who follows Peirce quite closely in certain respects, says that “a symbol is a sign…which acts as substitute for some other sign with which it is synonymous” and that “all signs not symbols are signals”.

The meaning of ‘meaning’

In this chapter I will make a number of general points and introduce certain distinctions which will be taken for granted in all that follows. The reader's attention is drawn especially to the fact that any term that is introduced here and given a technical interpretation will be used exclusively in that sense, in so far as it is employed as a technical term, throughout the book. Such terms will be marked with a following asterisk when they are introduced in their technical sense in this or succeeding chapters too. Asterisks will also be used occasionally to remind the reader that a term which has been introduced earlier is being employed in a technical sense and should not be interpreted in any of its nontechnical senses. All asterisked terms are explained in the body of the text or in the footnotes.

Semantics is generally defined as the study of meaning; and this is the definition that we will provisionally adopt: what is to be understood by ‘meaning’ in this context is one of our principal concerns in later chapters. Ever since Ogden and Richards (1923) published their classic treatise on this topic, and indeed since long before that, it has been customary for semanticists to emphasize the fact (and let us grant that it is a fact) that the noun ‘meaning’ and the verb ‘to mean’ themselves have many distinguishable meanings.

General attitudes

In this chapter we shall be concerned with behaviourist theories of meaning. Although behaviourism is nowadays less widely accepted than it was a decade or so ago, it was for a long time dominant in American psychology and it exercised a considerable influence upon the formulation and discussion of some of the basic issues in semantics, not only by psychologists, but also by certain linguists and philosophers.

It is perhaps useful to begin by distinguishing between behaviourism as a general attitude, on the one hand, and behaviourism as a fully developed psychological theory, on the other. In this section, we will discuss behaviourism in the more general sense, recognizing four characteristic principles or tendencies which give it its particular force or flavour.

First to be noted is a distrust of all mentalistic terms like ‘mind’, ‘concept’, ‘idea’, and so on, and the rejection of introspection as a means of obtaining valid data in psychology. The reason for the rejection of introspection is readily understood. Everyone's own personal thoughts and experience are private to him and what he will say about them to others is notoriously unreliable. Indeed, he is just as likely to deceive himself involuntarily as he is deliberately to mislead others about the beliefs and motives which inspire his conduct. Since this is so, the fact that there might be wide agreement among a number of persons reporting upon the results of their introspection is not a sufficient guarantee that these reports are trustworthy.

Introductory

In the first chapter of this book it was pointed out that the word ‘meaning’ had a number of distinguishable, but perhaps related, senses. Subsequently we drew a broad distinction between three kinds of meaning signalled by language: descriptive, social and expressive (2.4). In chapter 3 we saw that languages may be unique among natural semiotic systems in their capacity to transmit descriptive, as well as social and expressive, information. In this, as in the previous chapter, we shall be concerned solely with descriptive meaning.

Distinctions of the kind we shall be discussing have been drawn by many philosophers, but they have been drawn in a variety of ways. It is now customary, as we shall see, to draw a twofold distinction between what we will call sense* and reference*. Other terms used for the same, or at least a similar, contrast are: ‘meaning’ and ‘reference’ (where ‘meaning’ is given a narrower interpretation than it bears as an everyday p re-theoretical term); ‘connotation’ and ‘denotation’; ‘intension’ and ‘extension’.

No attempt will be made to compare systematically the usage of different authors. But it may be helpful to point out one or two of the terminological pitfalls for the benefit of readers who are not already familiar with the various senses in which the terms mentioned above are employed in the literature. The term ‘reference’, as we shall define it below, has to do with the relationship which holds between an expression and what that expression stands for on particular occasions of its utterance.

When I began writing this book six years ago, it was my intention to produce a fairly short one-volume introduction to semantics which might serve the needs of students in several disciplines and might be of interest to the general reader. The work that I have in fact produced is far longer, though in certain respects it is less comprehensive, than I originally anticipated; and for that reason it is being published in two volumes.

Volume 1 is, for the most part, more general than volume 2; and it is relatively self-contained. In the first seven chapters, I have done my best, within the limitations of the space available, to set semantics within the more general framework of semiotics (here defined as the investigation of both human and non-human signalling-systems); and I have tried to extract from what ethologists, psychologists, philosophers, anthropologists and linguists have had to say about meaning and communication something that amounts to a consistent, if rather eclectic, approach to semantics. One of the biggest problems that I have had in writing this section of the book has been terminological. It is frequently the case in the literature of semantics and semiotics that the same terms are employed in quite different senses by different authors or that there are several alternatives for what is essentially the same phenomenon. All I can say is that I have been as careful as possible in selecting between alternative terms or alternative interpretations of the same terms and, within the limits of my own knowledge of the field, in drawing the reader's attention to certain terminological pitfalls.

As far as I know there has been no attempt to relate generative semantics (GS) to intensional logic (IL) in a complete and systematic manner. Indeed at first sight one may well doubt that a relation can be established at all. So the first question we shall be concerned with here is with which parts of the theory of GS one should try to establish such a relation. And the second will be with which methods should be used.

If both theories could be formulated as formal, or mathematical theories, then we could try to construct mappings between them. As Montague (1970b) has shown, intensional languages and intensional logic can be formulated as mathematical theories. But I know of no formalization of GS.

Another systematic way to attack this problem is reduction, which means roughly, the embedding of one theory into another. This can be done for parts of theories as well and it is that approach I shall take here. To this extent then, no complete solution to the embedding problem will be given.

It is well known that Montague's theory contains both syntax and semantics (i.e. a model theory). Concerning the syntax of GS, Partee (1972), to give one example, has formulated transformations in a Montaguetype syntax. This does not mean that the syntax or the surface structure of both theories are comparable.

Abstract

Preference semantics (PS) is a set of formal procedures for representing the meaning structure of natural language, with a view to embodying that structure within a system that can be said to understand, rather than within what I would call the ‘derivational paradigm’, of transformational grammar (TG) and generative semantics (GS), which seeks to determine the wellformedness, or otherwise, of sentences. I argue that the distinction is not a trivial one, at least not if one genuinely wants to develop a model of human competence. For rejecting utterances is just what humans do not do. They try to understand them.

I outline a system of preference semantics that does this: in operation it has access to the senses of words coded as lexical decomposition trees, formed from a finite inventory of semantic primitives. For each phrase or clause of a complex sentence, the system builds up a network of such trees with the aid of structured items called templates and, at the next level, it structures those networks with higher level items called paraplates. At each stage the system directs itself towards the correct network by always opting for the most ‘semantically dense’ one it can construct. I suggest that this opting for the ‘greatest semantic density’ can be seen as an interpretation of Joos' (1972) ‘Semantic axiom number one’.

I argue that the analysis of quite simple examples requires the use of inductive rules of inference which cannot, theoretically cannot, be accommodated within the derivational paradigm.

In this paper, I am going to discuss two closely related phenomena, namely generic tense and generic noun phrases. By ‘generic tense’ I am referring to cases such as the following:

1. Beavers build dams

2. I write with my left hand

3. John smokes cigars

4. Dogs bark

5. The sun rises in the east

6. Oil floats on water

7. John does not speak German

8. A gentleman does not offend a lady

Examples of generic noun phrases are the italicized constituents in the following sentences:

1. Beavers build dams

2. A beaver builds dams

3. The beaver builds dams

I shall mainly be concerned with the types exemplified by (9) and (10), i.e. indefinite generic noun phrases.

I am going to claim in this paper that the common semantic property of all generic expressions is that they are used to express law-like, or nomic, statements. The first thing to be done is to make this concept clear. A suitable way of doing so to a linguistic audience may be by using the following example, taken from Chomsky and Halle (1968). Suppose only inhabitants of Tasmania survive a future war, they say. ‘It might then be a property of all then existing languages that pitch is not used to differentiate lexical items.’

I will discuss two theories about adjectives. The first theory dates from the late 1960s. It is stated in Montague (1970) and Parsons (1968). According to this theory the meaning of an adjective is a function which maps the meanings of noun phrases onto other such meanings; e.g. the meaning of clever is a function which maps the meaning of man into that of clever man, that of poodle onto that of clever poodle, etc. Predicative uses of adjectives are explained as elliptic attributive uses. Thus This dog is clever is analysed as This dog is a clever dog – or as This dog is a clever animal, or perhaps as This dog is a clever being. Which noun phrase ought to be supplied in this reduction of predicative to attributive use is in general not completely determined by the sentence itself, and to the extent that it is not, the sentence must be regarded as ambiguous.

The main virtue of this doctrine is that it enables us to treat, within a precise semantical theory for a natural language – as e.g. that of Montague – adjectives in such a way that certain sentences which are, or might well be, false are not branded by the semantics as logically true. Examples of such sentences are:

1. Every alleged thief is a thief

2. Every small elephant is small

3. If every flea is an animal, then every big flea is a big animal

Model theory is a mathematical technique for investigating certain properties of formal systems: properties such as consistency, completeness, the finite model property and having a decision procedure. Instead of looking for proofs based directly upon the formal system being studied, the method is to relate it to other formal systems whose properties are already known, by defining a translation from the former to the latter. Where this can be carried through, the systems thus related to the one under investigation are termed ‘models’ of it and known properties of the models can then be extrapolated to the new system. If a natural language or a fragment of a natural language constitutes a formal system, then the technique can be applied to it also, for the same purposes. There is now a prevalent impression among linguists, however, that model theory can provide a theory of meaning for natural language. The thesis of this paper is that any such hope will certainly be disappointed and that the mistake has arisen from confusion among mathematicians about the correct description of their own procedure.

This confusion is illustrated by the following descriptions of model theory from a recent book on mathematical logic: ‘Model theory is the study of the relations between languages and the world, or more precisely between formal languages and the interpretations of formal languages' (Crossley et al. (1972:20)). The idea which links these two descriptions is that interpretations of formal languages are not, as I have claimed, other formal languages, but structures, ‘the world’ being the structure which interprets a natural language.

The main objective of this paper is to discuss the correspondence between the semantic structure of sentences and a structuring of the universe of discourse in a given time-point of the discourse.

Some possibilities of a classification of presuppositions, assertions and also allegations with respect to the distinction between a given world (state of affairs) and the points of reference (pragmatic context of an utterance token) are analysed in section 1. Chomsky's use of the term ‘presupposition’ is rejected as misleading, since the topic (i.e. the elements not belonging to the focus of the sentence) refers to items not only known, but activated in the given time-point of the utterance (section 2). Chomsky's range of permissible focus is shown to be determined by the hierarchy of communicative dynamism of the sentence (given by a systemic ordering of participants of verbs in the grammar and by contextual boundness); his choice of focus corresponds to the placement of the juncture between contextually bound and non-bound elements (section 3). If the scale of communicative dynamism of the participants of a verb is denoted, in semantic representation (SR), by a linear ordering of the participants, and the placement of boundness juncture is included, too, then – as demonstrated on crucial examples in section 4 – a semantically-based generative description can be formulated in which neither global constraints nor semantically relevant transformations are needed.

Introduction

It is generally agreed that pronominalization and deletion under identity are closely related phenomena; Postal (1970) and Jackendoff (1972) have made particularly striking cases for the existence of close formal similarities among pronominalization, reflexivization, and coreferential complement subject deletion. Their claims are quite similar in spite of the differences between the generative and interpretive semantics frameworks, and both are concerned with complement subject deletion not only when it is controlled by the next higher verb, i.e. ordinary Equi-NP Deletion, but also when its ‘controller’ is several clauses away, i.e. what Grinder (1970) analysed as ‘Super-Equi NP Deletion’. What I want to explore in this paper is the relation between pronominalization and deletion in the ‘Super-Equi NP Deletion’ cases, as illustrated by (1) and (2).

1. Johni thought it was foolish to shave himselfi

2. Johni thought it was foolish for himi to shave himselfi

I am going to argue that (1) and (2) are not simply optional surface variants, but that their similarity rather results from an accidental convergence of quite disparate processes. If my argument is correct, then on a generative semantics approach (1) and (2) should have distinct underlying representations and on an interpretive approach their semantic interpretations should be arrived at by distinct interpretive principles, even though for this particular pair of examples there may be semantic rules which would show the two sentences to be logically equivalent.

Introduction

The objective towards which we are working is the development of a French Recognition Grammar (FRG) capable of being automatized. Apart from the purely formal aspects (development of the model, logicomathematical definition of the operators, writing the rules), such an enterprise must necessarily have its basis in a linguistic theory; in this work the essential linguistic concepts are borrowed from A. Culioli (see Culioli (1971) and Culioli, Fuchs, and Pecheux (1970)). The aim of this paper is not to expound or justify the theory, but rather to show how, from this theoretical starting point, the linguistic phenomenon of aspect can be treated within the framework of an FRG.

We shall note very briefly that the chief characteristic of the theory we adopt is that it takes into account the whole dimension of ‘utterance’. Our basic assumption is that syntactic structures (to which may be added an interpretation of the lexical units by means of semantic features) cannot on their own satisfactorily account for a certain number of phenomena such as the different roles of determiners, the choice of the passive as opposed to the active, the use of auxiliaries, tenses, ‘presenters’, etc. Even less can this level of explanation account for the ties of affinity or the rules of exclusion which exist among these different phenomena. Worse still: certain phenomena which seem at first sight to belong to the realm of syntax (e.g. complex sentences, relative clauses) can be treated solely in terms of structural concepts (e.g. ‘embedding’) only if one takes certain theoretical decisions which are likely to conceal more problems than they elucidate.

We shall propose in this paper a formal semantics for elementary embedded questions, such as John knows which student Mary invited, John can't remember who left early, etc. The semantics for these sentences will be stated in terms of that for the corresponding ‘direct’ questions, e.g. Which student did Mary invite?, Who left early?, etc. So I shall first review the semantics of elementary direct questions, as proposed in Keenan and Hull (1973), and then generalize the analysis to cover the case of embedded questions:

Direct questions

The intuition

We consider a question such as (1):

(1) Which student did Mary invite?

to be basically a request for the identification of the student who Mary invited. An answer to the question is, linguistically, a noun phrase that refers to that individual. It might be an alternative description such as the student who won first prize, or perhaps just an elementary referring expression such as John, or even him. If the noun phrase does refer to the student in question, then it is a true answer to the question; otherwise, it is not.

In our semantics, then, question-answer pairs determine truth values. Questions themselves are, semantically, the sort of thing that makes a proposition from an answer phrase, but they do not themselves carry truth values. The basis of our semantics of questions lies in the definition of truth and falsehood for question-answer pairs – that is, in the definition of the question-answer relation.