Can Proofs be Animated by Games?

Issue title: Typed Lambda Calculi and Applications 2005, Selected Papers

Article type: Research Article

Authors: Hayashi, Susumu

Affiliations: Humanistic Informatics, Graduate School of Letters, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto, 606-8501, Japan. E-mail: [email protected]

Abstract: Proof animation is a way of executing proofs to find errors in the formalization of proofs. It is intended to be "testing in proof engineering". Although the realizability interpretation as well as the functional interpretation based on limit-computations were introduced as means for proof animation, they were unrealistic as an architectural basis for actual proof animation tools. We have found a game theoretic semantics corresponding to these interpretations, which is likely to be the right architectural basis for proof animation.

Keywords: Game semantics, Computations in Classical Logic, Learning theory

Journal: Fundamenta Informaticae, vol. 77, no. 4, pp. 331-343, 2007