2011/05/31 by Giorgi Japaridze · 1 citation
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #acm:03B47 #acm:03B70 #acm:68Q10 #acm:68T15 #acm:68T27 #cs.LO #math.LO #msc:03B47 #msc:03B70 #msc:68Q10 #msc:68T15 #msc:68T27
paper · pdf · doi:10.1007/s00153-012-0313-8
published as Archive for Mathematical Logic 52 (2013), pp. 173-212
arxiv created 2012/09/19 · openalex publication_date 2012/11/22 · crossref created 2012/11/22 · crossref issued 2012/11/23 · crossref published 2012/11/23 · crossref published-online 2012/11/23 · crossref published-print 2013/02/01 · arxiv updated 2013/02/05 · openalex created_date 2016/06/24 · crossref deposited 2019/05/23 · crossref indexed 2025/10/28 · openalex updated_date 2026/07/29
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of negation, parallel conjunction, parallel disjunction, 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.