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

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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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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Jinan, China

    Giorgi Japaridze

  2. Department of Computing Sciences, Villanova University, Villanova, PA, USA

    Giorgi Japaridze

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  1. Giorgi Japaridze
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Correspondence to Giorgi Japaridze.

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Supported by 2010 Summer Research Fellowship from Villanova University.

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Japaridze, G. The taming of recurrences in computability logic through cirquent calculus, Part I. Arch. Math. Logic 52, 173–212 (2013). https://doi.org/10.1007/s00153-012-0313-8

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  • DOI: https://doi.org/10.1007/s00153-012-0313-8

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