Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Sequent and hypersequent calculi for abelian and łukasiewicz logics
ACM Transactions on Computational Logic (TOCL)
Proof Theory for Casari's Comparative Logics
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LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Disjunction property and complexity of substructural logics
Theoretical Computer Science
Proof analysis in intermediate logics
Archive for Mathematical Logic
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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 single-conclusion (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 Łukasiewicz logic is outlined.