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Archive for Mathematical Logic

, Volume 52, Issue 1–2, pp 213–259 | Cite as

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

  • Giorgi Japaridze
Article

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 previous) Part I containing preliminaries and a soundness proof, and (the present) Part II containing a completeness proof.

Keywords

Computability logic Cirquent calculus Interactive computation Game semantics Resource semantics 

Mathematics Subject Classification (2000)

Primary 03B47 Secondary 03B70 68Q10 68T27 68T15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyShandong UniversityJinanChina
  2. 2.Department of Computing SciencesVillanova UniversityVillanovaUSA

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