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The logic of interactive turing reduction

  • Giorgi Japaridze (a1)
  • DOI: http://dx.doi.org/10.2178/jsl/1174668394
  • Published online: 01 March 2014
Abstract
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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[2]A. Blass , A game semantics for linear logic, Annals of Pure and Applied Logic, vol. 56 (1992), pp. 183–220.

[3]W. Felscher , Dialogues, strategies, and intuitionistic provability, Annals of Pure and Applied Logic, vol. 28 (1985), pp. 217–254.

[5]K. Gödel , Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Dialectica, vol. 12 (1958), pp. 280–287.

[6]G. Japaridze , Introduction to computability logic, Annals of Pure and Applied Logic, vol. 123 (2003), pp. 1–99.

[8]G. Japaridze , From truth to computability I, Theoretical Computer Science, vol. 357 (2006), pp. 100–135.

[9]G. Japaridze , Propositional computability logic I, ACM Transactions on Computational Logic, vol. 7 (2006), no. 2, pp. 302–330.

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