Introduction to computability logic
type: Item
instance of: scholarly article
title: Introduction to computability logic
zbMATH Open document ID: 1028.03025
DOI: 10.1016/S0168-0072(03)00023-X
author: Giorgi Japaridze
published in: Annals of Pure and Applied Logic
publication date: 2003-09-25T00:00:00Z
review text: The intuitive notion of interactive computational problems is formalized as a sort of games between the machine and the environment (a user). Computability is understood as the existence of a Turing machine that wins the game against any possible environment. The used formalism is an \(n\)-disjoint union of the formalisms of classical, intuitionistic and linear logics, with logical operators interpreted as operations on problems. Validity of a formula is understood as being ``always computable''. The universal logic is the set of all valid formulas. This logic integrates, on the basis of one semantics, classical, intuitionistic and linear logics, with their seemingly unrelated or even antagonistic philosophies. The paper provides illustrations of potential applications of the universal logic in knowledge-based, resource-based and planning systems, as well as constructive applied theories.
Mathematics Subject Classification ID: 03B70
Mathematics Subject Classification ID: 03B47
Mathematics Subject Classification ID: 03F52
Mathematics Subject Classification ID: 91A80
Mathematics Subject Classification ID: 03F50
Mathematics Subject Classification ID: 68Q10
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 1985941
zbMATH Keywords: computability logic
zbMATH Keywords: interactive computation
zbMATH Keywords: game semantics
zbMATH Keywords: classical logic
zbMATH Keywords: linear logic
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: Turing machine
Wikidata QID: Q56765032
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1985941