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A Unified Sequent Calculus for Focused Proofs

Liang Chuck Dale Miller 1, 2 
2 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : We present a compact sequent calculus LKU for classical logic organized around the concept of polarization. Focused sequent calculi for classical logic, intuitionistic logic, and multiplicative-additive linear logic are derived as fragments of LKU by increasing the sensitivity of specialized structural rules to polarity information. We develop a unified, streamlined framework for proving cut-elimination in the various fragments. Furthermore, each sublogic can interact with other fragments through cut. We also consider the possibility of introducing classical-linear hybrid logics.
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Submitted on : Thursday, January 10, 2013 - 1:38:03 PM
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  • HAL Id : hal-00772347, version 1



Liang Chuck, Dale Miller. A Unified Sequent Calculus for Focused Proofs. LICS 2009 - Twenty-Fourth Annual IEEE Symposium on LOGIC IN COMPUTER SCIENCE, Aug 2009, Los Angeles, United States. ⟨hal-00772347⟩



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