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Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F14%3A00436118%21RIV15-GA0-67985807
rdf:type
n10:Vysledek skos:Concept
dcterms: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.
dcterms:title
A Duality for Distributive Unimodal Logic A Duality for Distributive Unimodal Logic
skos:prefLabel
A Duality for Distributive Unimodal Logic A Duality for Distributive Unimodal Logic
skos:notation
RIV/67985807:_____/14:00436118!RIV15-GA0-67985807
n3:aktivita
n18:P n18:I
n3:aktivity
I, P(GAP202/10/1826)
n3:dodaniDat
n19:2015
n3:domaciTvurceVysledku
n7:7847424
n3:druhVysledku
n16:D
n3:duvernostUdaju
n20:S
n3:entitaPredkladatele
n4:predkladatel
n3:idSjednocenehoVysledku
706
n3:idVysledku
RIV/67985807:_____/14:00436118
n3:jazykVysledku
n14:eng
n3:klicovaSlova
modal logic; distributive modal logic; intuitionistic modal logic; positive modal logic; bi-intuitionistic modal logic; duality theory
n3:klicoveSlovo
n5:bi-intuitionistic%20modal%20logic n5:positive%20modal%20logic n5:modal%20logic n5:intuitionistic%20modal%20logic n5:distributive%20modal%20logic n5:duality%20theory
n3:kontrolniKodProRIV
[20D033201F67]
n3:mistoKonaniAkce
Groningen
n3:mistoVydani
London
n3:nazevZdroje
Advances in Modal Logic
n3:obor
n8:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:projekt
n9:GAP202%2F10%2F1826
n3:rokUplatneniVysledku
n19:2014
n3:tvurceVysledku
Přenosil, Adam
n3:typAkce
n15:WRD
n3:zahajeniAkce
2014-08-05+02:00
s:numberOfPages
16
n13:hasPublisher
College Publications
n11:isbn
978-1-84890-151-3