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  1. Introduction to computability logic.Giorgi Japaridze - 2003 - Annals of Pure and Applied Logic 123 (1-3):1-99.
    This work is an attempt to lay foundations for a theory of interactive computation and bring logic and theory of computing closer together. It semantically introduces a logic of computability and sets a program for studying various aspects of that logic. The intuitive notion of computational problems is formalized as a certain new, procedural-rule-free sort of games between the machine and the environment, and computability is understood as existence of an interactive Turing machine that wins the game against any possible (...)
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  • Towards applied theories based on computability logic.Giorgi Japaridze - 2010 - Journal of Symbolic Logic 75 (2):565-601.
    Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with (...)
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  • The taming of recurrences in computability logic through cirquent calculus, Part I.Giorgi Japaridze - 2013 - Archive for Mathematical Logic 52 (1-2):173-212.
    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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  • A propositional system induced by Japaridze's approach to IF logic.W. Xu - 2014 - Logic Journal of the IGPL 22 (6):982-991.
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  • The taming of recurrences in computability logic through cirquent calculus, Part II.Giorgi Japaridze - 2013 - Archive for Mathematical Logic 52 (1-2):213-259.
    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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\neg}}$$\end{document}, parallel conjunction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\wedge}}$$\end{document}, parallel disjunction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\vee}}$$\end{document}, branching recurrence ⫰, and branching corecurrence ⫯. The article is published in two parts, with (the previous) (...)
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  • A cirquent calculus system with clustering and ranking.Wenyan Xu - 2016 - Journal of Applied Logic 16:37-49.
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  • Introduction to clarithmetic III.Giorgi Japaridze - 2014 - Annals of Pure and Applied Logic 165 (1):241-252.
    The present paper constructs three new systems of clarithmetic : CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete with respect to PA-provably recursive time computability. This is in the sense that an arithmetical problem A has a τ-time solution for some PA-provably recursive function τ iff A is represented by some theorem of CLA8. System CLA9 is shown to be sound and intensionally complete with respect to constructively PA-provable computability. This is in the sense (...)
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  • Soundness and completeness of the Cirquent calculus system CL6 for computability logic.Wenyan Xu & Sanyang Liu - 2012 - Logic Journal of the IGPL 20 (1):317-330.
    Computability logic is a formal theory of computability. The earlier article ‘Introduction to cirquent calculus and abstract resource semantics’ by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic. The present article extends that result to the more expressive cirquent calculus system CL6, which is a conservative extension of both CL5 and classical propositional logic.
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