Intuitionistic computability logic

Japaridze, Giorgi: Intuitionistic computability logic. Acta cybernetica, (18) 1. pp. 77-113. (2007)

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Abstract

Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible language, where formulas represent computational problems and "truth" is understood as algorithmic solvability, CL potentially offers a comprehensive logical basis for constructive applied theories and computing systems inherently requiring constructive and computationally meaningful underlying logics. Among the best known constructivistic logics is Heyting's intuitionistic calculus INT, whose language can be seen as a special fragment of that of CL. The constructivistic philosophy of INT, however, just like the resource philosophy of linear logic, has never really found an intuitively convincing and mathematically strict semantical justification. CL has good claims to provide such a justification and hence a materialization of Kolmogorov's known thesis "INT = logic of problems". The present paper contains a soundness proof for INT with respect to the CL semantics.

Item Type: Article
Event Title: Kalmár Workshop on Logic in Computer Science, 2003, Szeged
Journal or Publication Title: Acta cybernetica
Date: 2007
Volume: 18
Number: 1
Page Range: pp. 77-113
ISSN: 0324-721X
Language: angol
Uncontrolled Keywords: Természettudomány, Informatika
Additional Information: Bibliogr.: p. 112-113.; Abstract
Date Deposited: 2016. Oct. 15. 12:25
Last Modified: 2018. Jun. 05. 13:56
URI: http://acta.bibl.u-szeged.hu/id/eprint/12805

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