Game semantics
From Exampleproblems
Game semantics (German: Dialogische Logik) is an approach to the semantics of logic that bases the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. Paul Lorenzen, in the late 1950s, was the first to introduce a game semantics for logic. Since then, numerous sorts of game semantics have been introduced and studied in logic, and have been applied to the formal semantics of programming languages.
The primary motivation for Lorenzen and his student Kuno Lorenz was to find a game-semantical, or dialogue-semantical (as they preferred to call it) justification for intuitionistic logic. Blass was the first to point out connections between game semantics and linear logic. This line was further developed by Samson Abramsky, Radhakrishnan Jagadeesan, Martin Hyland, Luke Ong and others. Japaridze started treating games as foundational entities in their own right, elaborating a concept of games that formalizes the intuitive notion of interactive computational problems, and basing his computability logic on such games.
Recently it has been championed by Jaakko Hintikka and Gabriel Sandu especially for Independence-friendly logic (more recently Information-friendly logic) or a logic of branching (or partially ordered) quantifiers. It was thought that the principle of compositionality fails for these logics and hence Tarskian truth definitions would not provide a suitable semantics. The meaning of quantifiers were thus given by game-theoretical means where a universal quantifier represents the choice by one player (sometimes called the "falsifier") of a value from the domain while the existential quantifier represents the choice by another player (sometimes called the "verifier") of a value from the domain. Wilfred Hodges has given a compositional semantics and showed that the two semantics are equivalent for IF-logics.
See also
articles
- Erik C. W. Krabbe: Dialogue Foundations: Dialogue Logic Revisited. Source: Supplement to the Proceedings of The Aristotelian Society, Volume 75, Number 1, July 2001, pp. 33-49(17) Publisher: Blackwell Publishing
