Focusing and Polarization in Intuitionistic Logic

Chuck Liang 1 Dale Miller 2
2 PARSIFAL - Proof search and reasoning with logic specifications
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof search and the proof normalization approaches to computation. Various proof systems in literature exhibit characteristics of focusing to one degree or another. We present a new, focused proof system for intuitionistic logic, called LJF, and show how other proof systems can be mapped into the new system by inserting logical connectives that prematurely stop focusing. We also use LJF to design a focused proof system for classical logic. Our approach to the design and analysis of these systems is based on the completeness of focusing in linear logic and on the notion of polarity that appears in Girard's LC and LU proof systems.
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Submitted on : Thursday, August 16, 2007 - 7:19:32 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
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  • HAL Id : inria-00167231, version 1
  • ARXIV : 0708.2252



Chuck Liang, Dale Miller. Focusing and Polarization in Intuitionistic Logic. Computer Science Logic, Sep 2007, Lausanne, Switzerland. ⟨inria-00167231⟩



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