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The logic of interactive Turing reduction

Giorgi Japaridze
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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. See http://www.cis.upenn.edu/~giorgi/cl.html for a comprehensive online source on computability logic.

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Giorgi Japaridze. 2006-02-11. The logic of interactive Turing reduction. https://doi.org/10.2178/jsl/1174668394

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