Languages for Imperfect Information

This chapter gives a self-contained introduction to game-theoretical semantics (GTS) both for classical first-order logic and for one of its extensions, Independence-Friendly Logic (IF logic). The games used for the interpretation of IF logic are 2-player win-lose extensive games of imperfect information. Several game-theoretical phenomena will be discussed in this context, including signaling and indeterminacy. To overcome indeterminacy, we introduce mixed strategies and apply Von Neumann’s Minimax Theorem. This results in a probabilistic interpretation of IF sentences (equilibrium semantics). We shall use IF logic and its equilibrium semantics to model some well known examples which involve games with imperfect information: Lewis’ signaling games and Monty Hall.

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