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Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F12%3A00379885%21RIV13-GA0-67985807
rdf:type
skos:Concept n14:Vysledek
dcterms: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.
dcterms:title
Distributive substructural logics as coalgebraic logics over posets Distributive substructural logics as coalgebraic logics over posets
skos:prefLabel
Distributive substructural logics as coalgebraic logics over posets Distributive substructural logics as coalgebraic logics over posets
skos:notation
RIV/67985807:_____/12:00379885!RIV13-GA0-67985807
n14:predkladatel
n15:ico%3A67985807
n3:aktivita
n9:Z n9:P n9:I
n3:aktivity
I, P(GAP202/11/1632), Z(AV0Z10300504)
n3:dodaniDat
n10:2013
n3:domaciTvurceVysledku
n12:6922287 n12:6286615
n3:druhVysledku
n21:D
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n13:predkladatel
n3:idSjednocenehoVysledku
131628
n3:idVysledku
RIV/67985807:_____/12:00379885
n3:jazykVysledku
n18:eng
n3:klicovaSlova
substructural logics; frame semantics; coalgebras; coalgebraic logic; Goldblatt-Thomason theorem
n3:klicoveSlovo
n4:substructural%20logics n4:Goldblatt-Thomason%20theorem n4:frame%20semantics n4:coalgebras n4:coalgebraic%20logic
n3:kontrolniKodProRIV
[63B83F4EFEC4]
n3:mistoKonaniAkce
Copenhagen
n3:mistoVydani
London
n3:nazevZdroje
Advances in Modal Logic
n3:obor
n16:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:projekt
n6:GAP202%2F11%2F1632
n3:rokUplatneniVysledku
n10:2012
n3:tvurceVysledku
Bílková, Marta Velebil, J. Horčík, Rostislav
n3:typAkce
n7:WRD
n3:zahajeniAkce
2012-08-22+02:00
n3:zamer
n20:AV0Z10300504
s:numberOfPages
24
n19:hasPublisher
College Publications
n17:isbn
978-1-84890-068-4