Toward a general frame semantics for modal many-valued logics
The result's identifiers
Result code in 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>
Alternative codes found
RIV/67985807:_____/19:00491819
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Toward a general frame semantics for modal many-valued logics
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-04630S" target="_blank" >GA17-04630S: Predicate graded logics and their applications to computer science</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Soft Computing
ISSN
1432-7643
e-ISSN
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Volume of the periodical
23
Issue of the periodical within the volume
7
Country of publishing house
DE - GERMANY
Number of pages
9
Pages from-to
2233-2241
UT code for WoS article
000461580400009
EID of the result in the Scopus database
2-s2.0-85049671436