Towards the Automated Generation of Focused Proof Systems
Abstract
This paper tackles the problem of formulating and proving the completeness of focusedlike proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search nondeterminism. We demonstrate that it is possible to construct a complete focused proof system from a given unfocused 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.04177
 Bibcode:
 2015arXiv151104177N
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 In Proceedings WoF'15, arXiv:1511.02529