On Polarity Frames: Applications to Substructural and Lattice-Based Logics

0439788 - ÚI 2015 RIV GB eng C - Konferenční příspěvek (zahraniční konf.)
Suzuki, Tomoyuki
On Polarity Frames: Applications to Substructural and Lattice-Based Logics.
Advances in Modal Logic. London: College Publications, 2014 - (Goré, T.; Kooi, B.; Kurucz, A.), s. 533-552. 10. ISBN 978-1-84890-151-3.
[Advances in Modal Logic. Groningen (NL), 05.08.2014-08.08.2014]
Grant CEP: GA ČR GAP202/10/1826
Institucionální podpora: RVO:67985807
Klíčová slova: relational semantics * substructural and lattice-based logics * lattice expansions * topological characterisation * Goldblatt-Thomason's theorem * amalgamation property
Kód oboru RIV: BA - Obecná matematika
http://www.aiml.net/volumes/volume10/Suzuki.pdf

In this paper, on one hand, we address topology on polarities via general polarity frames by analogy of the relationship between topology on sets and general Kripke frames. Based on the topology on polarities, we provide the topological characterisation of descriptive polarity frames. On the other hand, we introduce disjoint unions and amalgamations of polarity frames with additional relations and constants. As applications of these constructions, we establish the Goldblatt-Thomason's theorem for (distributive) substructural logic and the amalgamation property for some lattice- based algebras.
Trvalý link: http://hdl.handle.net/11104/0242979