About: Distributive substructural logics as coalgebraic logics over posets

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We show how to understand frame semantics of distributive substructural logics coalgebraically, thus opening a possibility to study them as coalgebraic logics. As an application of this approach we prove a general version of Goldblatt-Thomason theorem that characterizes definability of classes of frames for logics extending the distributive Full Lambek logic, as e.g. relevance logics, many-valued logics or intuitionistic logic. The paper is rather conceptual and does not claim to contain significant new results. We consider a category of frames as posets equipped with monotone relations, and show that they can be understood as coalgebras for an endofunctor of the category of posets. In fact, we adopt a more general definition of frames that allows to cover a wider class of distributive modal logics. Goldblatt-Thomason theorem for classes of resulting coalgebras for instance shows that frames for axiomatic extensions of distributive Full Lambek logic are modally definable classes of certain coalgebras, the respective modal algebras being precisely the corresponding subvarieties of distributive residuated lattices. We show how to understand frame semantics of distributive substructural logics coalgebraically, thus opening a possibility to study them as coalgebraic logics. As an application of this approach we prove a general version of Goldblatt-Thomason theorem that characterizes definability of classes of frames for logics extending the distributive Full Lambek logic, as e.g. relevance logics, many-valued logics or intuitionistic logic. The paper is rather conceptual and does not claim to contain significant new results. We consider a category of frames as posets equipped with monotone relations, and show that they can be understood as coalgebras for an endofunctor of the category of posets. In fact, we adopt a more general definition of frames that allows to cover a wider class of distributive modal logics. Goldblatt-Thomason theorem for classes of resulting coalgebras for instance shows that frames for axiomatic extensions of distributive Full Lambek logic are modally definable classes of certain coalgebras, the respective modal algebras being precisely the corresponding subvarieties of distributive residuated lattices. (en)
Title	Distributive substructural logics as coalgebraic logics over posets Distributive substructural logics as coalgebraic logics over posets (en)
skos:prefLabel	Distributive substructural logics as coalgebraic logics over posets Distributive substructural logics as coalgebraic logics over posets (en)
skos:notation	RIV/67985807:_____/12:00379885!RIV13-GA0-67985807
http://linked.open...avai/riv/aktivita	I P Z
http://linked.open...avai/riv/aktivity	I, P(GAP202/11/1632), Z(AV0Z10300504)
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Bílková, Marta Horčík, Rostislav
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
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	131628
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/12:00379885
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	substructural logics; frame semantics; coalgebras; coalgebraic logic; Goldblatt-Thomason theorem (en)
http://linked.open.../riv/klicoveSlovo	substructural logics Goldblatt-Thomason theorem coalgebras frame semantics coalgebraic logic
http://linked.open...ontrolniKodProRIV	[63B83F4EFEC4]
http://linked.open...v/mistoKonaniAkce	Copenhagen
http://linked.open...i/riv/mistoVydani	London
http://linked.open...i/riv/nazevZdroje	Advances in Modal 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	Algebraic Methods in Proof Theory
http://linked.open...UplatneniVysledku	2012
http://linked.open...iv/tvurceVysledku	Bílková, Marta Horčík, Rostislav Velebil, J.
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2012-08-22 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
number of pages	24 (xsd:int)
http://purl.org/ne...btex#hasPublisher	College Publications
https://schema.org/isbn	978-1-84890-068-4

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