towards the automated generation of focused proof systems

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ID: 225168
2015
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Abstract
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.
Reference Key
nigam2015electronictowards Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Vivek Nigam;Giselle Reis;Leonardo Lima
Journal ama journal of ethics
Year 2015
DOI
10.4204/EPTCS.197.1
URL
http://arxiv.org/pdf/1511.04177v1
Keywords
computer science mathematicselectronic computers

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