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The logic of interactive turing reduction

Published online by Cambridge University Press:  12 March 2014

Giorgi Japaridze
Giorgi Japaridze*
Affiliation:
Villanova University, Department of Computing Sciences, 800 Lancaster Avenue, Villanova, PA 19085, USA. E-mail: giorgi.japaridze@villanova.edu URL: http://www.csc.villanova.edu/&U0007E;japaridz/
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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.

Keywords

Computability logicIntuitionistic logicInteractive computationGame semantics
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 243 - 276
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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