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Distributive substructural logics as coalgebraic logics over posets
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SYSNO ASEP 0379885 Druh ASEP C - Konferenční příspěvek (mezinárodní konf.) Zařazení RIV D - Článek ve sborníku Název Distributive substructural logics as coalgebraic logics over posets Tvůrce(i) Bílková, Marta (UIVT-O) SAI, RID, ORCID
Horčík, Rostislav (UIVT-O) SAI, RID
Velebil, J. (CZ)Zdroj.dok. Advances in Modal Logic. - London : College Publications, 2012 / Bolander T. ; Braüner T. ; Moss L. ; Ghilardi S. - ISBN 978-1-84890-068-4 Rozsah stran s. 119-142 Poč.str. 24 s. Forma vydání Tištěná - P Akce Advances in Modal Logic Datum konání 22.08.2012-25.08.2012 Místo konání Copenhagen Země DK - Dánsko Typ akce WRD Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova substructural logics ; frame semantics ; coalgebras ; coalgebraic logic ; Goldblatt-Thomason theorem Vědní obor RIV BA - Obecná matematika CEP GAP202/11/1632 GA ČR - Grantová agentura ČR Institucionální podpora UIVT-O - RVO:67985807 CEZ AV0Z10300504 - UIVT-O (2005-2011) EID SCOPUS 84904294531 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2013
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