The Logic of Interactive Turing Reduction

Journal of Symbolic Logic 72 (1):243 - 276 (2007)
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Abstract

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic reduction. This concept — more precisely, the associated concept of reducibility — is a generalization of Turing reducibility from the traditional, input/output sorts of problems to computational tasks of arbitrary degrees of interactivity

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In the Beginning was Game Semantics?Giorgi Japaridze - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo, Games: Unifying Logic, Language, and Philosophy. Dordrecht, Netherland: Springer Verlag. pp. 249--350.
Towards applied theories based on computability logic.Giorgi Japaridze - 2010 - Journal of Symbolic Logic 75 (2):565-601.

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