Toward a general frame semantics for modal many-valued logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F19%3A00491819" target="_blank" >RIV/67985556:_____/19:00491819 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/19:00491819

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00500-018-3369-5" target="_blank" >http://dx.doi.org/10.1007/s00500-018-3369-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-018-3369-5" target="_blank" >10.1007/s00500-018-3369-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Toward a general frame semantics for modal many-valued logics

Popis výsledku v původním jazyce

Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general A-frames over a given residuated lattice AA (i.e., the usual frames with a collection of admissible A-valued sets). We describe in detail the relation between general Kripke and neighborhood A-frames and prove that, if the logic of A is finitary, all extensions of the corresponding logic E of A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems.

Název v anglickém jazyce

Toward a general frame semantics for modal many-valued logics

Popis výsledku anglicky

Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general A-frames over a given residuated lattice AA (i.e., the usual frames with a collection of admissible A-valued sets). We describe in detail the relation between general Kripke and neighborhood A-frames and prove that, if the logic of A is finitary, all extensions of the corresponding logic E of A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA17-04630S" target="_blank" >GA17-04630S: Predikátové škálované logiky a jejich aplikace v informatice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Soft Computing

ISSN

1432-7643

e-ISSN

—

Svazek periodika

23

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

9

Strana od-do

2233-2241

Kód UT WoS článku

000461580400009

EID výsledku v databázi Scopus

2-s2.0-85049671436