The logic of interactive Turing reduction
Giorgi Japaridze
Source: J. Symbolic Logic Volume 72, Issue 1
(2007), 243-276.
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1174668394
Digital Object Identifier: doi:10.2178/jsl/1174668394
Mathematical Reviews number (MathSciNet): MR2298481
Zentralblatt MATH identifier: 1161.03015
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