Neighborhood semantics for modal many-valued logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00480886" target="_blank" >RIV/67985556:_____/18:00480886 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/18:00480886

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.fss.2017.10.009" target="_blank" >http://dx.doi.org/10.1016/j.fss.2017.10.009</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2017.10.009" target="_blank" >10.1016/j.fss.2017.10.009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Neighborhood semantics for modal many-valued logics

Popis výsledku v původním jazyce

The majority of works on modal many-valued logics consider Kripke-style possible worlds frames as the principal semantics despite their well-known axiomatizability issues when considering non-Boolean accessibility relations. The present work explores a more general semantical picture, namely a many-valued version of the classical neighborhood semantics. We present it in two levels of generality. First, we work with modal languages containing only the two usual unary modalities, define neighborhood frames over algebras of the logic FLew with operators, and show their relation with the usual Kripke semantics (this is actually the highest level of generality where one can give a straightforward definition of the Kripke-style semantics). Second, we define generalized neighborhood frames for arbitrary modal languages over a given class of algebras for an arbitrary protoalgebraic logic and, assuming certain additional conditions, axiomatize the logic of all such frames (which generalizes the completeness theorem of the classical modal logic E with respect to classical neighborhood frames).

Název v anglickém jazyce

Neighborhood semantics for modal many-valued logics

Popis výsledku anglicky

The majority of works on modal many-valued logics consider Kripke-style possible worlds frames as the principal semantics despite their well-known axiomatizability issues when considering non-Boolean accessibility relations. The present work explores a more general semantical picture, namely a many-valued version of the classical neighborhood semantics. We present it in two levels of generality. First, we work with modal languages containing only the two usual unary modalities, define neighborhood frames over algebras of the logic FLew with operators, and show their relation with the usual Kripke semantics (this is actually the highest level of generality where one can give a straightforward definition of the Kripke-style semantics). Second, we define generalized neighborhood frames for arbitrary modal languages over a given class of algebras for an arbitrary protoalgebraic logic and, assuming certain additional conditions, axiomatize the logic of all such frames (which generalizes the completeness theorem of the classical modal logic E with respect to classical neighborhood frames).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF15-34650L" target="_blank" >GF15-34650L: Modelování vágních kvantifikátorů v matematické fuzzy logice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

345

Číslo periodika v rámci svazku

15 August

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

99-112

Kód UT WoS článku

000436569200006

EID výsledku v databázi Scopus

2-s2.0-85031759745