Expanding the Realm of Systematic Proof Theory

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Expanding the Realm of Systematic Proof Theory
Abstract. This paper is part of a general project of developing a systematic and algebraic proof theory for nonclassical logics. Generalizing our previous work on intuitionistic-substructural axioms and singleconclusion (hyper)sequent calculi, we define a hierarchy on Hilbert axioms in the language of classical linear logic without exponentials. We then give a systematic procedure to transform axioms up to the level P′ 3 of the hierarchy into inference rules in multiple-conclusion (hyper)sequent calculi, which enjoy cut-elimination under a certain condition. This allows a systematic treatment of logics which could not be dealt with in the previous approach. Our method also works as a heuristic principle for finding appropriate rules for axioms located at levels higher than P′ 3. The case study of Abelian and Lukasiewicz logic is outlined.
Agata Ciabattoni, Lutz Straßburger, Kazushig
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CSL
Authors Agata Ciabattoni, Lutz Straßburger, Kazushige Terui
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