A Duality for Distributive Unimodal Logic

Kód výsledku v 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>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

A Duality for Distributive Unimodal Logic

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

A Duality for Distributive Unimodal Logic

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Matematická fuzzy logika v informatice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Advances in Modal Logic

ISBN

978-1-84890-151-3

ISSN

—

e-ISSN

—

Počet stran výsledku

16

Strana od-do

423-438

Název nakladatele

College Publications

Místo vydání

London

Místo konání akce

Groningen

Datum konání akce

5. 8. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—