Since the first chapter of this book presents an intro duction to the present state of game-theoretical semantics (GTS), there is no point in giving a briefer survey here. Instead, it may be helpful to indicate what this volume attempts to do. The first chapter gives a short intro duction to GTS and a survey of what is has accomplished. Chapter 2 puts the enterprise of GTS into new philo sophical perspective by relating its basic ideas to Kant's phi losophy (...) of mathematics, space, and time. Chapters 3-6 are samples of GTS's accomplishments in understanding different kinds of semantical phenomena, mostly in natural languages. Beyond presenting results, some of these chapters also have other aims. Chapter 3 relates GTS to an interesting line of logical and foundational studies - the so-called functional interpretations - while chapter 4 leads to certain important methodological theses. Chapter 7 marks an application of GTS in a more philo sophical direction by criticizing the Frege-Russell thesis that words like "is" are multiply ambiguous. This leads in turn to a criticism of recent logical languages (logical notation), which since Frege have been based on the ambi guity thesis, and also to certain methodological sug gestions. In chapter 8, GTS is shown to have important implications for our understanding of Aristotle's doctrine of categories, while chapter 9 continues my earlier criticism of Chomsky's generative approach to linguistic theorizing. (shrink)

In this work formal systems suitable for the development of a model of inquiry are investigated. We append to a sequent-version of a tableau deductive system new rules for adding formulas to a tableau construction which represent the acquisition of information concerning a given model of the initial premises. These rules may be thought of as enabling an inquirer to ask questions of a source of information about the model. ;We begin by showing how the derivability relation for various of (...) the resulting systems is related to derivability in standard deductive systems. We next look at the way these so-called interrogative systems differ from deductive systems with respect to the basic metatheoretical properties: soundness, completeness, transitivity, etc. We finally begin the development of a theory of interrogative definability, or identifiability. (shrink)

In any survey of recent developments in semantics, the game-theoretic approach to the semantics of both formal and of natural languages which has been developed by Jaakko Hintikka and his associates must loom large. It is indeed well known by this time that the semantics of the usual first-order logic can be spelled out in terms of games. What is not equally generally known is that this game-theoretical semantics can be augmented so as to apply also to natural languages and (...) not only to some of the artificial languages studied by logicians. The results already reached by Hintikka and his associates in this direction nevertheless show that many important phenomena of natural language can be handled in the game-theoretical framework. In this paper I shall first try to outline the basic ideas of the game-theoretical approach to semantics, then discuss briefly some problems which have so far been left untouched and thereby try to provide some new evidence for the naturalness and adequacy of a game-theoretical semantics. (shrink)

This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...

The structure of strategies for semantical games is studied by means of a new formalism developed for the purpose. Rigorous definitions of strategy, winning strategy, truth, and falsity are presented. Non-contradiction and bivalence are demonstrated for the truth-definition. The problem of the justification of deduction is examined from this perspective. The rules of a natural deduction system are justified: they are seen to guarantee existence of a winning strategy for the defender in the semantical game for the conclusion, given winning (...) strategies for that player in the games for the premises. Finally, it is shown how semantical games and the truth-definition can be given for languages lacking individual constants. *** DIRECT SUPPORT *** AZ902009 00003. (shrink)