2015/11/07 by Vivek Nigam, Giselle Reis, Leonardo Lima
Computer Science · Mathematics · #Advanced Database Systems and Queries #Combinatorial proof #Completeness (order theory) #Computer science #Discrete mathematics #Formal Methods in Verification #Graph #Linear logic #Logic, programming, and type systems #Mathematical proof #Mathematics #Permutation (music) #Permutation graph #Proof calculus #Proof complexity #Proof theory #Structural proof theory #Theoretical computer science #cs.LO
paper · pdf · doi:10.4204/eptcs.197.1
published as EPTCS 197, 2015, pp. 1-6 · In Proceedings WoF'15, arXiv:1511.02529
openalex publication_date 2015/11/07 · arxiv created 2015/11/13 · arxiv updated 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search non-determinism. We demonstrate that it is possible to construct a complete focused proof system from a given un-focused proof system if it satisfies some conditions. Our key idea is to generalize the completeness proof based on permutation lemmas given by Miller and Saurin for the focused linear logic proof system. This is done by building a graph from the rule permutation relation of a proof system, called permutation graph. We then show that from the permutation graph of a given proof system, it is possible to construct a complete focused proof system, and additionally infer for which formulas contraction is admissible. An implementation for building the permutation graph of a system is provided. We apply our technique to generate the focused proof systems MALLF, LJF and LKF for linear, intuitionistic and classical logics, respectively.