Journal of Symbolic Logic

The logic of interactive Turing reduction

Giorgi Japaridze

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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.

Article information

J. Symbolic Logic, Volume 72, Issue 1 (2007), 243-276.

First available in Project Euclid: 23 March 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}
Secondary: 03F50: Metamathematics of constructive systems 03B70: Logic in computer science [See also 68-XX] 68Q10: Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85] 68T27: Logic in artificial intelligence 68T30: Knowledge representation 91A05: 2-person games

Computability logic Intuitionistic logic Interactive computation Game semantics


Japaridze, Giorgi. The logic of interactive Turing reduction. J. Symbolic Logic 72 (2007), no. 1, 243--276. doi:10.2178/jsl/1174668394.

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