Jack Kulas

AnyProblems — No Problems

This paper is a development and extension of the semantical theory for natural languages proposed and developed by the senior author under the name of game-theoretical semantics (GTS).1 The topics discussed include the general explanatory strategies for natural-language semantics employed by GTS, the treatment of negation in GTS, and the thesis that the English quantifier-word “any” is always to be considered a universal quantifier. We shall start with no-problems and then consider any-problems, all the while keeping an eye on methodological considerations.

Semantical Games, Subgames, and Functional Interpretations

There is a way of looking at game-theoretical semantics (GTS) that is not directly related either to its philosophical motivation or to some of its linguistic applications, but that establishes potentially interesting links between it and certain developments in logic and in the foundations of mathematics.1 These links have not been examined in detail in the literature, but they appear extremely promising. In order to see these links, a certain idea introduced into GTS by Hintikka and Carlson is needed: the idea of a subgame.2

Definite Descriptions in Game-Theoretical Semantics

The many attractive features of Russell’s treatment of definite descriptions, or as we shall also call them, the-phrases, make its failure as an overall theory ever so poignant.1 This failure needs few comments. Even if, pace Strawson, Russell’s theory works perfectly when applied to definite descriptions like “the present King of France”, it fail to account for the uses of the-phrases that pick up earlier reference. We shall call these the anaphoric uses of the-phrases. (1) is an example of such a use:

Introduction to Game-Theoretical Semantics

This introductory part presents enough of the basic ideas of game-theoretical semantics (GTS) to serve as a basis for a new theory of anaphoric pronouns to be presented in Part III, below. Not all of the details will actually be needed for the account we are going to offer of the semantics of anaphoric pronouns, but since the attractiveness of our account is partly due to its being an aspect of a more comprehensive systematic theory, it is in order to sketch the basic ideas of game-theoretical semantics in general.

Comparisons with Other Treatments

The three differences (i)-(iii) listed above in sec. 21 between our theory and most other approaches enable us to make certain comparisons here. In historical perspective, it is perhaps not entirely unfair to say that one of the aims of recent treatments of anaphora has been to explain such exceptions to the Langacker-Ross condition that from our perspective are caused by (i)-(iii), especially by (ii)-(iii). One theoretical difference between our theory and some of the other current theories is that, in these competing theories, an attempt is made to account for the exceptions by reference to the syntactical structure of the input sentence S0 of a semantical game. From our perspective, this may be expected to be doubly misleading (a) because some of the exceptions are caused by factors that are essentially semantical, not syntactical, such as the Exclusion Principle; and (b) because the relevant syntactical structure is not that of Ss, anyway, but that of some different sentence making its appearance at a later stage of the semantical game that originally started from S0.

GTS Explains Coreference Restrictions

The inadequacies of the received notion of coreference do not, of course, imply that all its uses in the literature are worthless. However, the legitimate uses can in many cases be captured by our theory, given a deeper foundation, and in some cases improved on.

General Theoretical Issues

One of the accounts competing with ours assimilates anaphoric pronouns that have quantifier phrases as their antecedents to the bound variables of quantification theory. It is therefore in order to discuss such uses of anaphoric pronouns.

A Game-Theoretical Approach to Anaphora

Let us return to our main question. How, then, do anaphoric pronouns operate? How can they operate, if the grammatical relation of a pronoun to its antecedent is not relied on? An interesting alternative is suggested by our treatment of anaphoric the-phrases expounded in the second part of this book (cf., Hintikka and Kulas 1982, 1983, forthcoming; Kulas 1982). Instead of relying on the grammatical relation between an anaphoric the-phrase and its antecedent, that treatment relies on a contextually given set of entities, called /. Its members are not grammatical objects, but entities of the kind one’s language speaks of. This set is not determined by the definite-article phrase alone, nor is it determined in conjunction with the sentence S in question. It is not constant for all the the-phrases occurring in one and the same S. It consists essentially of those individuals (of the appropriate category) that have been picked out in the semantical game G(S) associated with S (or otherwise available to the players) at the time a rule is applied to the the-phrase in question in the game.

The Exclusion Principle

As was noted in the second part of this book, both anaphorically used the-phrases and anaphoric pronouns are subject to an additional restriction. The tacit quantifiers governing the choice of b in (G. he) and (G. anaphoric the) have to be understood as being partially exclusive (cf. Hintikka 1973, chap. 1). More precisely, the choice of b in (G. he) (and in (G. anaphoric the)) must be restricted by excluding all individuals whose proper names, interpreted by having had (G. name) applied to them, occur in the same clause as (i.e., are, syntactically speaking, dominated by precisely the same S-nodes as) the pronoun (or the definite description) to which a game rule is being applied, at the stage of the game when a rule is applied to it. This general principle — we shall call it the “Exclusion Principle” — can be generalized to cover expressions other than pronouns that are evaluated by applying some game rule to them.