Philosophy Lexicon of Arguments

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Game-theoretical Semantics: game-theoretical semantics does not trace back truth or falsity of sentences, to meanings alone, but to strategies of verification, which are understood as winning strategies. See also situation semantics, possible world semantics, Kripke-Semantics, Montague-Semantics, dialogical logic.

Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

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I 25
Definition game-theoretical semantics/GTS/notation/Hintikka: here the truth of a proposition S in a model M is explained as the existence of a winning strategy in a game of verification (semantic game G (S)).
I: I am the verifier.
Nature/Opponent: nature or opponent is the falsifier.
I 26
(G.E) when the game of the sentence (Ex) has reached S[x] and M, I choose an individual, e.g. b from the domain do/(M) of W. Then the game is continued with respect to S 8b] and M.
(G.U.) in the same way, except that here nature chooses the individual b.
(G.v) G(S1 v S2) (played in M) starts with my choice of vo Si (i = 1 or 2) The rest of the game is
G (Si) (played in the same model m)
G.&) Similarly, except that the nature selects Si.
(G.~) G (~S) is like G (S) except that the rules of the two players (I and nature) have been exchanged.
(G.K.) When the game reaches the set {b} KS and the model (possible world) M0, nature chooses an epistemic b-alternative M1 to M0. The game continues with regard to S and M1.
Game-theoretical semantics/GTS/Hintikka: with game-theoretical semantics the semantics can be executed explicitly for branched formulas like (4.6.). They show the informational independence.
In (4.6), the steps associated with "(Ex) and ([b] K" are made without the knowledge of the other step.
In general, each step is linked to an information set that contains the other steps the player knows when he takes the step.
Order: therefore, the structure of the operators of a sentence does not always have to be ordered partially at all. ((s). That is, the order of (Ex) and "knows" may be arbitrary.
I 27
Game-theoretical semantics/Informational Independence/Hintikka: game-theoretical semantics shows how other basic concepts of a language can also be independent of epistemic operators.
For example, an atomic predicate A (x) or a name can be judged independently in M of an epistemic operator, e.g. "knows". ((s) "b knows that x runs" (but not that it is Paul, though x = Paul)).
Solution/Hintikka: since the actual referents must be assigned in the winning strategy, expressions like
A (x) / {b} K) and
A / {b} K
actually pick out the actual referents in M0.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.

Hin I
Jaakko Hintikka
Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989

J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996

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Ed. Martin Schulz, access date 2018-05-24