Download PDFOpen PDF in browserCuts for circular proofs4 pages•Published: July 28, 2014AbstractOne of the authors introduced in [1] a calculus ofcircular proofs for studying the computability arising from the following categorical operations: finite products and coproducts, initial algebras, final coalgebras. The calculus of [1] is cut-free; yet, even if sound and complete for provability, it lacks an important property for the semantics of proofs, namely fullness w.r.t. the class of natural categorical models called μ-bicomplete category in [2]. We fix, with this work, this problem by adding the cut rule to the calculus. To this goal, we need to modifying the syntactical constraints on the cycles of proofs so to ensure soundness of the calculus and at same time local termination of cut-elimination. The enhanced proof system fully represents arrows of the intended model, a free μ-bicomplete category. We also describe a cut-elimination procedure as a model of computation arising from the above mentioned categorical operations. The procedure constructs a cut-free proof-tree with infinite branches out of a finite circular proof with cuts. [1] Luigi Santocanale. A calculus of circular proofs and its categorical semantics. In Mogens Nielsen and Uffe Engberg, editors, FoSSaCS, volume 2303 of Lecture Notes in Computer Science, pages 357–371. Springer, 2002. [2] Luigi Santocanale. μ-bicomplete categories and parity games. Theoretical Informatics and Applications, 36:195–227, September 2002. Keyphrases: categorical proof theory, fixpoints, inductive and coinductive types, initial and final (co)algebras In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 72-75.
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