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2008

Presentation of a Game Semantics for First-Order Propositional Logic

Mimram, Samuel

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Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies.

In this article, we introduce a game semantics for a fragment of first order propositional logic.
One of the main difficulties that has to be faced when constructing such semantics is to make them precise by characterizing definable strategies - that is strategies which actually behave like a proof.
This characterization is usually done by restricting to the model to strategies satisfying subtle combinatory conditions such as innocence, whose preservation under composition is often difficult to show.

Presentation of a Game Semantics for First-Order Propositional Logic · Around

Built on

Categorical Algebra
S. MacLane · 1965
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Categories for the Working Mathematician
S. MacLane · 1971
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Limits indexed by category-valued 2-functors
R. Street · 1976
Earlier work this paper cites.
The Free Adjunction
S. Schanuel and R. Street · 1986
Earlier work this paper cites.
The Geometry of Tensor Calculus, I
A. Joyal and R. Street · 1991
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