On Game Semantics of the Affine and Intuitionistic Logics

Authors:
Ilya Mezhirov;Nikolay Vereshchagin
Affiliations:
The German Research Center for Artificial Intelligence, TU Kaiserslautern,;Lomonosov Moscow State University, Leninskie Gory, 119991
Venue:
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Year:
2008

Citing 4
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Linear logic

Theoretical Computer Science
Variants of Realizability for Propositional Formulas and the Logic of the Weak Law of Excluded Middle

CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Introduction to Cirquent Calculus and Abstract Resource Semantics* This material is based upon work supported by the National Science Foundation under Grant No. 0208816, and 2005 Summer Research Grant from Villanova University.

Journal of Logic and Computation
Intuitionistic computability logic

Acta Cybernetica

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Abstract

We show that the uniform validity is equivalent to the non-uniform validity for both Blass' semantics of [1] and Japaridze's semantics of [5] (thus proving a conjecture from [5]). We present a shorter proof (than that of [10]) of the completeness of the positive fragment of intuitionistic logic for both these semantics. Finally, we show that validity for the "parallel recurrence" version of Japaridze's semantics of [5] is equivalent to accomplishability in the sense of [4].