Page 350 - Encyclopedia of Philosophy of Language

Formal Semantics
Montague R 1973 The proper treatment of quantification in ordinary English. In: Hintikka K J J, Moravscik J M E, Suppes P (eds.) Approaches to Natural Language. Reidel, Dordrecht
Muskens R 1989 Meaning and partiality. (PhD thesis. Uni- versity of Amsterdam)
Muskens R 1991 Anaphora meaning, context and the logic of change. In: Eijck J van (ed.), Logics in AI. Springer, Berlin
Partee B H 197S Montague Grammar and Transformational Grammar. Lin 6:203-300
Partee B H (ed.) 1975 Montague Grammar. Academic Press, New York
Percy W 1954 The Message in the Bottle. Farrar, Straus and Giroux, New York
Pereira F, Shieber S 1985 Prolog and Natural Language Analysis. CSLI Lecture Notes 10, Stanford, CA (Dis- tributed by University of Chicago Press, Chicago, IL)
Tarski A 1956 The concept of truth in formalized languages. In: Tarski A (trans. Woodger J H) Logic,Semantics,Mela- mathematics Papersfrom 1923to 1938. Clarendon Press, Oxford
Van Benthem J F A K. 1986 Essays in Logical Semantics. Reidel, Dordrecht
Van Benthem J 1991 General dynamics. Theoretical Linguis- tics: 159-201
The term 'game-theoretical semantics' is used to refer to systems of formal semantics in which the semantic rules are formulated as rules in a game of some kind. The term 'game-theoretical' suggests a rather direct connection to mathematical game theory as developed by von Neumann and others, the main source of inspi- ration for extant proposals for game-theoretical sem- antics has rather been Wittgenstein's concept of 'language game' than game theory.
Although the notion of a language game has been employed in semantics by various people over the years, the term 'game-theoretical semantics' is mainly associated with the work of Jaakko Hintikka and his followers. Hintikka first developed his system of game-theoretical semantics for formal languages but later applied it also to natural language. The rules given below are Hintikka's (1983) for first-order predi- cate calculus, but the rules for ordinary English would be analogous.
The semantical game in terms of which a sentence S is interpreted in Hintikka's system involves two players, called 'Myself' or T and 'Nature,' whose aims in the game are to show that S is true and false, respectively. Complex sentences are interpreted step- wise, by applying the game rules in a top-down fashion, until an atomic sentence is reached. If it is true, I/My- self have won; if it is false, Nature has won. Another way of expressing this is to say that a sentence is true if there is a winning strategy for 'Myself in the game; if it is false, there is a winning strategy for 'Nature.'
The rules applied are the following:
(a) (G. A) If A is atomic, I have won if A is true
and Nature has won if A is false.
(b) (G. &) G (S, & S2) begins by Nature's choice of
S, of S2. The rest of the game is G(S,) or G(S2) respectively.
(c) (G. v ) G(S1 v S2) begins by Myself's choice of SI or S2. The rest of the game is G(S1) or G(S2) respectively.
(d) (G. V)G(Vx(S(x)) begins by Nature's choice of a member of the domain. Let the name of the member chosen be arbitrarily determined as 'b.' The rest of the game is then G(S(b)).
(e) (G. 3) G(3x(S(x)) is denned likewise except that the member of the domain is chosen by Myself.
(f) (G.—) G(—S) is played like G(S) except that the roles of the two players (as defined by these
rules) are interchanged.
Hintikka attributes particular significance to the
treatment of quantifiers in his semantics. It is meant to make explicit the intuition that an existential sen- tence is true if a value can be found for the existentially bound variable that makes the sentence in the scope of the quantifier true. In the rule above, this is for- mulated in terms of 'Myself choosing a value for the variable. In the case of the universal quantifier, it is 'Nature' that makes the choice.
Hintikka's theory of game-theoretical semantics has been applied to various problems in semantics, notably branching quantifiers, the choice between some and any in English, 'donkey sentences,' inten- tional identity, tense, and others.
Bibliography
Hintikka J 1973 Logic, Language-Games, and Information: Kantian Themes in the Philosophy of Logic. Clarendon Press, Oxford
Hintikka J (in collaboration with Kulas J) 1983 The Game of Language. D Reidel, Dordrecht
Saarinen E (ed.) 1979 Game-theoretical Semantics. D Reidel, Dordrecht
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Game-theoretical Semantics O.Dahl