Journal of Symbolic Logic

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.

Article information

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

Dates
First available: 23 March 2007

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

Subjects
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

Keywords
Computability logic Intuitionistic logic Interactive computation Game semantics

Citation

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


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