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2 results on '"contraction-free"'

1. Structural Interactions and Absorption of Structural Rules in BI Sequent Calculus

Author

Arisaka, Ryuta, Proof search and reasoning with logic specifications (PARSIFAL), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France

Subjects
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, 000 Computer science, knowledge, general works, contraction-free, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], proof theory, cut elimination, Logic in Computer Science (cs.LO), Mathematics::Logic, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, sequent calculus, TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS, Computer Science::Logic in Computer Science, BI, Computer Science
Abstract

Development of a contraction-free BI sequent calculus, be the contraction-freeness implicit or explicit, has not been successful in the literature. We address this problem by presenting such a sequent system. Our calculus involves no structural rules. It should be an insight into non-formula contraction absorption in other non-classical logics. Contraction absorption in sequent calculus is associated to simpler cut elimination and to efficient proof searches.

Published
2014

2. A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic

Author

Brian Hill, Francesca Poggiolesi, Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH), Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS), Vrije Universiteit Brussel (VUB), Institut d'Histoire et de Philosophie des Sciences et des Techniques (IHPST), Université Paris 1 Panthéon-Sorbonne (UP1)-Département d'Etudes Cognitives - ENS Paris (DEC), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Contraction-free, Propositional Dynamic Logic, Logic, Cut-elimination theorem, Zeroth-order logic, 0102 computer and information sciences, 01 natural sciences, History and Philosophy of Science, Proof calculus, [SHS.ECO.ECO]Humanities and Social Sciences/Economics and Finance/domain_shs.eco.eco, Computer Science::Logic in Computer Science, Tree-hypersequent, Calculus, [INFO]Computer Science [cs], Sequent, 0101 mathematics, Mathematics, Propositional variable, Discrete mathematics, Natural deduction, 010102 general mathematics, Noncommutative logic, Proof theory, [SHS.PHIL]Humanities and Social Sciences/Philosophy, Sequent calculus, Mathematics::Logic, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, 010201 computation theory & mathematics, TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS, Cut-free
Abstract

International audience; In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infini-tary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.

Published
2010

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