The taming of recurrences in computability logic through cirquent calculus, Part I

Archive for Mathematical Logic 52 (1-2):173-212 (2013)
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Abstract

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of negation ${\neg}$ , parallel conjunction ${\wedge}$ , parallel disjunction ${\vee}$ , branching recurrence ⫰, and branching corecurrence ⫯. The article is published in two parts, with (the present) Part I containing preliminaries and a soundness proof, and (the forthcoming) Part II containing a completeness proof

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10.1007/s00153-012-0313-8

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Citations of this work

The Parallel versus Branching Recurrences in Computability Logic.Wenyan Xu & Sanyang Liu - 2013 - Notre Dame Journal of Formal Logic 54 (1):61-78.
A Propositional Cirquent Calculus for Computability Logic.Giorgi Japaridze - 2024 - Journal of Logic, Language and Information 33 (4):363-389.

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References found in this work

A game semantics for linear logic.Andreas Blass - 1992 - Annals of Pure and Applied Logic 56 (1-3):183-220.
A constructive analysis of RM.Arnon Avron - 1987 - Journal of Symbolic Logic 52 (4):939 - 951.
Introduction to computability logic.Giorgi Japaridze - 2003 - Annals of Pure and Applied Logic 123 (1-3):1-99.
In the Beginning was Game Semantics?Giorgi Japaridze - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo, Games: Unifying Logic, Language, and Philosophy. Dordrecht, Netherland: Springer Verlag. pp. 249--350.
The Logic of Interactive Turing Reduction.Giorgi Japaridze - 2007 - Journal of Symbolic Logic 72 (1):243 - 276.

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