Focusing Strategies in the Sequent Calculus of Synthetic Connectives

  • Authors:
  • Kaustuv Chaudhuri

  • Affiliations:
  • INRIA Saclay - Île-de, France

  • Venue:
  • LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
  • Year:
  • 2008

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Abstract

It is well-known that focusing striates a sequent derivation into phases of like polarity where each phase can be seen as inferring a synthetic connective. We present a sequent calculus of synthetic connectives based on neutral proof patterns, which are a syntactic normal form for such connectives. Different focusing strategies arise from different polarisations and arrangements of synthetic inference rules, which are shown to be complete by synthetic rule permutations. A simple generic cut-elimination procedure for synthetic connectives respects both the ordinary focusing and the maximally multi-focusing strategies, answering the open question of cut-admissibility for maximally multi-focused proofs.