# Reasoning about reasoning about games

## Melvin Fitting

### Lehman College - CUNY Graduate Center

A mixture of propositional dynamic logic and epistemic logic that we call PDL + E is used to give a formalization of Artemovâ€™s knowledge based reasoning approach to game theory. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both syntactic proofs and semantical arguments. Formal proofs are used establish what is the case and what is needed to show this. Semantical machinery is used to establish what cannot be the case. All this makes a case that PDL + E can be a useful basis for the logical investigation of game theory.

Lehman College Professor Melvin Fitting received the Herbrand Award of 2012 for his groundbreaking contributions to the field of automated theorem proving, which focuses on getting computer programs to prove logical and mathematical deductions.