A Duality for Distributive Unimodal Logic

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F14%3A00436118" target="_blank" >RIV/67985807:_____/14:00436118 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A Duality for Distributive Unimodal Logic
Original language 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. Palmigianoand 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
Czech name
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Czech description
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Project
<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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