INTRODUCTION

The integration of syntactic and semantic processing has prompted a number of different architectures for natural language systems, such as rule-by-rule interpretation [221], semantic grammars [22] and cascaded ATNs [253]. The relationship between syntax and semantics has also been of central concern in theoretical linguistics, particularly following Richard Montague's work. Also, with the recent rapprochement between theoretical and computational linguistics, Montague's interpretation scheme has made its way into natural language systems. Variations on Montague's interpretation scheme have been adopted and implemented in several syntactic theories with a significant following in computational linguistic circles. The first steps in this direction were taken by Hobbs and Rosenschein [89]. A parser for LFG was augmented with a Montagovian semantics by Halvorsen [76]. GPSG has been similarly augmented by Gawron et al. [65], and Schubert and Pelletier [206] followed with a compositional interpretation scheme using a first order logic rather than Montague's computationally intractable higher-order intensional logic.

In parallel with these developments in the syntax/semantics interface, unification-based mechanisms for linguistic description had significant impact both on syntactic theory and syntactic description. But the Montagovian view of compositionality in semantics and the architectures for configuring the syntax/semantics interface were slower to achieve a similar revaluation in view of unification and the new possibilities for composition which it brought.

INTRODUCTION

This chapter concerns experiments with Situation Schemata as a linguistic representation language, in the first instance for Machine Translation purposes but not exclusively so. The work reported is primarily concerned with the adaptation of the Situation Schemata language presented by Fenstad et al. [56] (but see also Fenstad et al. in this volume) to an implementation within grammars having interestingly broad linguistic coverage. We shall also consider the computational tools required for such an implementation and our underlying motivation. The chapter is therefore not solely concerned with the form of the representation language and its relation to any eventual interpretation language, but also with practical and methodological issues associated with the implementation of current theories in Computational Linguistics. A key theme is the interplay between linguistic information, representation and appropriate mechanisms for abstraction.

The rest of the chapter is divided into three further sections. Section 7.2 suggests that the problem of translation can shed light on a range of representational issues on the syntax/semantics border; it contains a brief introduction to Situation Semantics and the original version of Situation Schemata. Section 7.3 outlines the design of a computational toolkit for experimenting with unification-based descriptions, concentrating on details of the grammar formalism and its abstraction mechanisms. Section 7.4 considers the form of Situation Schemata that has been implemented within a grammar of German and some related representational issues that arise out of this work.

INTRODUCTION

Computational semantics lies at the intersection of three disciplines: linguistics, logic and computer science. A natural language system should provide a coherent framework for relating linguistic form and semantic content, and the relationship must be algorithmic.

There have been several important pairwise interactions, as detailed below, between linguistics and computer science, linguistics and logic, and logic and computer science. The point of computational semantics is the insistence on relating all three simultaneously. This is necessary from a cognitive as well as a knowledge engineering point of view.

LINGUISTICS AND COMPUTER SCIENCE

N. Chomsky's Syntactic Structures [34] signalled a renewal of theoretical linguistics, which for some of its theoretical tools drew upon automata and formal language theory. A link was soon established with the emerging computer science, leading to a vigorous field of computational linguistics, focusing on questions of linguistic form, i.e. syntax and morphology. This has proved to be of lasting value for the study of both natural and programming languages.

LINGUISTICS AND LOGIC

Language is more than linguistic form. R. Montague, in a series of papers starting from 1967 (see Thomason [219]), showed how to use the insights from logical semantics to ‘tame’ the meaning component of a natural language. Montague's tool was the model theory of higher order intensional logic. And he convincingly demonstrated how the use of this model theory could explain a wide range of linguistic phenomena.

THE PROBLEMS OF BELIEF REVISION

An Example

Suppose that you have a database that contains, among other things, the following pieces of information (in some form of code):

α: All European swans are white.

β: The bird caught in the trap is a swan.

γ: The bird caught in the trap comes from Sweden.

δ: Sweden is part of Europe.

If your database is coupled with a program that can compute logical inferences in the given code, the following fact is derivable from α – δ:

ε: The bird caught in the trap is white.

Now suppose that, as a matter of fact, the bird caught in the trap turns out to be black. This means that you want to add the fact –ε, i.e., the negation of ε, to the database. But then the database becomes inconsistent. If you want to keep the database consistent, which is normally a sound methodology, you need to revise it. This means that some of the beliefs in the original database must be retracted. You don't want to give up all of the beliefs since this would be an unnecessary loss of valuable information. So you have to choose between retracting α, β, γ or δ.

The problem of belief revision is that logical considerations alone do not tell you which beliefs to give up, but this has to be decided by some other means.

INTRODUCTION

Studies of the dynamics of (rational) belief have reached a new degree of sophistication through the formal models developed in particular by Levi (1980) and by Alchourrón, Gärdenfors, and Makinson (the AGM model, Alchourrón et al. 1985 and Gärdenfors 1988). In these models, an individual's beliefs are represented by a set that is closed under logical consequence. The AGM model and its underlying assumptions have had a profound influence on the study of belief base updating in computer science. Although states of belief are, for obvious reasons, represented in computer applications by finite sets of sentences, it is common to demand that “results from an update must be independent of the syntax of the original K[nowledge] B[ase]” (Katsuno and Mendelzon 1989). In other words, operations on finite sets are treated more or less as shadows of operations on the (infinite) logical closures of these sets.

In this paper, a different representation of beliefs will be introduced. A formalized belief state will consist of an ordered pair <K,Cn>. K, or the belief base, is a set of expressions that is not necessarily closed under logical consequence. It represents the basic facts on which an individual grounds her beliefs. Cn is a consequence operator, such that Cn(K) represents her beliefs (namely both the elements of K and the conclusions she draws from them).

INTRODUCTION

In the last five years, there has been much concern in Artificial Intelligence about the problem of belief revision. A rather exciting feature of the on-going debate is that it has led to an interaction between fields which usually ignore each other, such as logic, probability theory, fuzzy set and possibility theory, and their epistemological underpinnings. In his book, Gärdenfors (1988) emphasizes in a convincing way that notions of epistemic state can be defined in the framework of logic as well as in the one of probability theory and that similar postulates can be put forward in the two settings, for the purpose of devising rational updating operations that take place upon the arrival of new pieces of information. On the other hand Spohn (1988), in trying to refine the logical notion of epistemic state, viewed as a consistent and deductively closed set of propositions, comes close to Shackle's (1961) notions of degrees of potential surprise, as well as Zadeh's (1978) possibility theory. However he proposes revision rules that are in some way in accordance with probability theory where probabilities only take infinitesimal values (Spohn, 1990). Besides, one of the main outcomes of Gärdenfors' logical theory of belief change is that any revision process underlies an ordering of propositions that form the epistemic state; the rationality postulates force this ordering to satisfy specific properties, and the only numerical set-functions that can account for these properties are the so-called necessity measures that play a basic role in possibility theory (Dubois and Prade, 1988).

Knowledge update has been a matter of concern to two quite separate traditions: one in philosophical logic, and another in artificial intelligence. In this paper we draw on both traditions to develop a theory of update, based on conditional logic, for a kind of knowledge base that has proven to be of interest in artificial intelligence. After motivating and formulating the logic on which our theory is based, we will prove some basic results and show how our logic can be used to describe update in an environment in which knowledge bases can be treated as truth-value assignments in four-valued logic. In keeping with Nuel Belnap's terminology in Belnap (1977a) and Belnap (1977b), we will refer to such truth-value assignments as set-ups or as four-valued set-ups.

Paraconsistency, primeness, and atomistic update

For the moment we will not say exactly what a four-valued set-up is. Instead we will describe informally some conditions under which it would be natural to structure one's knowledge base as a four-valued set-up. One of these conditions has to do with the treatment of inconsistent input; a second has to do with the representation of disjunctive information; the third concerns what kinds of statements can be the content of an update.

Inconsistent input

A logical calculus is paraconsistent if it cannot be used to derive arbitrary conclusions from inconsistent premises. Belnap argues in general terms that paraconsistent reasoning is appropriate any context where an automated reasoner must operate without any guarantee that its input is consistent, and where nondegenerate performance is desirable even if inconsistency is present. Knowledge bases used in AI applications are cases of this sort.

INTRODUCTION

This chapter describes a model of autonomous belief revision (ABR) which discriminates between possible alternative belief sets in the context of change. The model determines preferred revisions on the basis of the relative persistence of competing cognitive states. It has been implemented as ICM (increased coherence model); a belief revision mechanism encompassing a three-tiered ordering structure which represents a blend between coherence and foundational theories of belief revision.

The motivation for developing the model of ABR is as a component of a model of communication between agents. The concern is choice about changing belief. In communication, agents should be designed to choose whether as well as how to revise their beliefs. This is an important aspect of design for multi-agent contexts as open environments (Hewitt, 1986), in which no one element can be in possession of complete information of all parts of the system at all times. Communicated information cannot therefore be assumed to be reliable and fully informed. The model of ABR and system ICM, represent the first phase in the development of a computational model of cooperative, yet autonomously determined communication. The theory of ABR and communication is explicated in section 2.

Section 3 follows with an outline of the problem of multiple alternative revisions, and a discussion of preference and strength of belief issues from an AI perspective. This section includes the relevant comparative and theoretical background for understanding the model of ABR described in section 4.

INTRODUCTION

Consider a knowledge base represented by a theory ψ of some logic, say propositional logic. We want to incorporate into ψ a new fact, represented by a sentence μ of the same language. What should the resulting theory be? A growing body of work (Dalal 1988, Katsuno and Mendelzon 1989, Nebel 1989, Rao and Foo 1989) takes as a departure point the rationality postulates proposed by Alchourrón, Gärdenfors and Makinson (1985). These are rules that every adequate revision operator should be expected to satisfy. For example: the new fact μ must be a consequence of the revised knowledge base.

In this paper, we argue that no such set of postulates will be adequate for every application. In particular, we make a fundamental distinction between two kinds of modifications to a knowledge base. The first one, update, consists of bringing the knowledge base up to date when the world described by it changes. For example, most database updates are of this variety, e.g. “increase Joe's salary by 5%”. Another example is the incorporation into the knowledge base of changes caused in the world by the actions of a robot (Ginsberg and Smith 1987, Winslett 1988, Winslett 1990). We show that the AGM postulates must be drastically modified to describe update.

The second type of modification, revision, is used when we are obtaining new information about a static world.

INTRODUCTION

There are many ways to change a theory. The tasks of adding a sentence to a theory and of retracting a sentence from a theory are non-trivial because they are usually constrained by at least three requirements. The result of a revision or contraction of a theory should again be a theory, i.e., closed under logical consequence, it should be consistent whenever possible, and it should not change the original theory beyond necessity. In the course of the Alchourrón-Gärdenfors-Makinson research programme, at least three different methods for constructing contractions of theories have been proposed. Among these the “safe contraction functions” of Alchourrón and Makinson (1985, 1986) have played as it were the role of an outsider. Gärdenfors and Makinson (1988, p. 88) for instance state that ‘another, quite different, way of doing this [contracting and revising theories] was described by Alchourrón and Makinson (1985).’ (Italics mine.) The aim of the present paper is to show that this is a miscasting.

In any case, it seems that the intuitions behind safe contractions are fundamentally different from those behind its rivals, the partial meet contractions of Alchourrón, Gärdenfors and Makinson (1985) and the epistemic entrenchment contractions of Gärdenfors and Makinson (1988). Whereas the latter notions are tailored especially to handling theories (as opposed to sets of sentences which are not closed under a given consequence operation), safe contraction by its very idea focusses on minimal sets of premises sufficient to derive a certain sentence.

INTRODUCTION

Belief revision is the process of incorporating new information into a knowledge base while preserving consistency. Recently, belief revision has received a lot of attention in AI, which led to a number of different proposals for different applications (Ginsberg 1986; Ginsberg, Smith 1987; Dalal 1988; Gärdenfors, Makinson 1988; Winslett 1988; Myers, Smith 1988; Rao, Foo 1989; Nebel 1989; Winslett 1989; Katsuno, Mendelzon 1989; Katsuno, Mendelzon 1991; Doyle 1990). Most of this research has been considerably influenced by approaches in philosophical logic, in particular by Gärdenfors and his colleagues (Alchourrón, Gärdenfors, Makinson 1985; Gärdenfors 1988), who developed the logic of theory change, also called theory of epistemic change. This theory formalizes epistemic states as deductively closed theories and defines different change operations on such epistemic states.

Syntax-based approaches to belief revision to be introduced in Section 3 have been very popular because of their conceptual simplicity. However, there also has been criticisms since the outcome of a revision operation relies an arbitrary syntactic distinctions (see, e.g., (Dalal 1988; Winslett 1988; Katsuno, Mendelzon 1989))—and for this reason such operations cannot be analyzed on the knowledge level. In (Nebel 1989) we showed that syntax-based approaches can be interpreted as assigning higher relevance to explicitly represented sentences. Based on that view, one particular kind of syntax-based revision, called base revision, was shown to fit into the theory of epistemic change. In Section 4 we generalize this result to prioritized bases.

INTRODUCTION

Recent years have seen considerable work on two approaches to belief revision: the so-called foundations and coherence approaches. The foundations approach supposes that a rational agent derives its beliefs from justifications or reasons for these beliefs: in particular, that the agent holds some belief if and only if it possesses a satisfactory reason for that belief. According to the foundations approach, beliefs change as the agent adopts or abandons reasons. The coherence approach, in contrast, maintains that pedigrees do not matter for rational beliefs, but that the agent instead holds some belief just as long as it logically coheres with the agent's other beliefs. More specifically, the coherence approach supposes that revisions conform to minimal change principles and conserve as many beliefs as possible as specific beliefs are added or removed. The artificial intelligence notion of reason maintenance system (Doyle, 1979) (also called “truth maintenance system”) has been viewed as exemplifying the foundations approach, as it explicitly computes sets of beliefs from sets of recorded reasons. The so-called AGM theory of Alchourrón, Gärdenfors and Makinson (1985; 1988) exemplifies the coherence approach with its formal postulates characterizing conservative belief revision.

Although philosophical work on the coherence approach influenced at least some of the work on the foundations approach (e.g., (Doyle, 1979) draws inspiration from (Quine, 1953; Quine and Ullian, 1978)), Harman (1986) and Gärdenfors (1990) view the two approaches as antithetical. Gärdenfors has presented perhaps the most direct argument for preferring the coherence approach to the foundations approach.

INTRODUCTION

Since the beginning of artificial intelligence research on action, researchers have been concerned with reasoning about actions with preconditions and postconditions. Through the work of Moore (1980), Pratt's (1980) dynamic semantics soon established itself in artificial intelligence as the appropriate semantics for action. Mysteriously, however, actions with preconditions and postconditions were not given a proper treatment within the modal framework of dynamic logic. This paper offers such an analysis. Things are complicated by the need to deal at the same time with the notion of competence, or an actor's ability. Below, a logic of actions with preconditions and postconditions is given a sound and complete syntactic characterization, in a logical formalism in which it is possible to express actor competence, and the utility of this formalism is demonstrated in the generation and evaluation of plans.

The notion of actions with pre- and postconditions arose in artificial intelligence in the field of planning. In formulating a plan to reach some particular goal, there are a number of things which a planning agent must take into account. First, he will have to decide which actions can and may be undertaken in order to reach the goal. The physical, legal, financial and other constraints under which an actor must act will be lumped together below, since we will be interested in what is common to them all, namely that they restrict available options.