About: Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL (which we call SL) has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP-based. This presentation is then used to obtain, in a uniform way applicable to most (both associative and nonassociative) substructural logics, a form of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics (i.e., logics complete with respect to linearly ordered algebras). Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL (which we call SL) has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP-based. This presentation is then used to obtain, in a uniform way applicable to most (both associative and nonassociative) substructural logics, a form of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics (i.e., logics complete with respect to linearly ordered algebras). Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. (en)
Title	Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties (en)
skos:prefLabel	Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties Nonassociative Substructural Logics and Their Semilinear Extensions: Axiomatization and Completeness Properties (en)
skos:notation	RIV/67985807:_____/13:00395361!RIV14-GA0-67985807
http://linked.open...avai/predkladatel	Ústav informatiky AV ČR, v.v.i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GBP202/12/G061)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Cintula, Petr Horčík, Rostislav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	91906
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/13:00395361
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	nonassociative full Lambek calculus; deduction theorem; standard completeness (en)
http://linked.open.../riv/klicoveSlovo	deduction theorem nonassociative full Lambek calculus standard completeness
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[617B9BC639E1]
http://linked.open...i/riv/nazevZdroje	Review of Symbolic Logic
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Center of excellence - Institute for theoretical computer science (CE-ITI)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	6
http://linked.open...iv/tvurceVysledku	Cintula, Petr Horčík, Rostislav Noguera, Carles
http://linked.open...ain/vavai/riv/wos	000323167200002
issn	1755-0203
number of pages	30 (xsd:int)
http://bibframe.org/vocab/doi	10.1017/S1755020313000099

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