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

Authors:
Giorgi Japaridze
Affiliations:
School of Computer Science and Technology, Shandong University, Jinan, China and Department of Computing Sciences, Villanova University, Villanova, USA
Venue:
Archive for Mathematical Logic
Year:
2013

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Archive for Mathematical Logic

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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 驴, and branching corecurrence 驴. 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.