About: A Duality for Distributive Unimodal Logic

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We introduce distributive unimodal logic as a modal logic of binary relations over posets which naturally generalizes the classical modal logic of binary relations over sets. The relational semantics of this logic is similar to the relational semantics of intuitionistic modal logic and positive modal logic, but it generalizes both of these by placing no restrictions on the accessibility relation. We introduce a corresponding quasivariety of distributive lattices with modal operators and prove a completeness theorem which embeds each such algebra in the complex algebra of its canonical modal frame. We then extend this embedding to a duality theorem which unies and generalizes the duality theorems for intuitionistic modal logic obtained by A. Palmigiano and for positive modal logic obtained by S. Celani and A. Jansana. As a corollary to this duality theorem, we obtain a Hennessy-Milner theorem for bi- intuitionistic unimodal logic, which is the expansion of distributive unimodal logic by bi-intuitionistic connectives. We introduce distributive unimodal logic as a modal logic of binary relations over posets which naturally generalizes the classical modal logic of binary relations over sets. The relational semantics of this logic is similar to the relational semantics of intuitionistic modal logic and positive modal logic, but it generalizes both of these by placing no restrictions on the accessibility relation. We introduce a corresponding quasivariety of distributive lattices with modal operators and prove a completeness theorem which embeds each such algebra in the complex algebra of its canonical modal frame. We then extend this embedding to a duality theorem which unies and generalizes the duality theorems for intuitionistic modal logic obtained by A. Palmigiano and for positive modal logic obtained by S. Celani and A. Jansana. As a corollary to this duality theorem, we obtain a Hennessy-Milner theorem for bi- intuitionistic unimodal logic, which is the expansion of distributive unimodal logic by bi-intuitionistic connectives. (en)
Title	A Duality for Distributive Unimodal Logic A Duality for Distributive Unimodal Logic (en)
skos:prefLabel	A Duality for Distributive Unimodal Logic A Duality for Distributive Unimodal Logic (en)
skos:notation	RIV/67985807:_____/14:00436118!RIV15-GA0-67985807
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP202/10/1826)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Přenosil, Adam
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	706
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/14:00436118
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	modal logic; distributive modal logic; intuitionistic modal logic; positive modal logic; bi-intuitionistic modal logic; duality theory (en)
http://linked.open.../riv/klicoveSlovo	duality theory modal logic bi-intuitionistic modal logic distributive modal logic intuitionistic modal logic positive modal logic
http://linked.open...ontrolniKodProRIV	[20D033201F67]
http://linked.open...v/mistoKonaniAkce	Groningen
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	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Matematická fuzzy logika v informatice
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Přenosil, Adam
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2014-08-05 (xsd:date)
number of pages	16 (xsd:int)
http://purl.org/ne...btex#hasPublisher	College Publications
https://schema.org/isbn	978-1-84890-151-3

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