Expressivity of Many-Valued Modal Logics, Coalgebraically
Result description
We apply methods developed to study coalgebraic logic to investigate expressivity of many-valued modal logics which we consider as coalgebraic languages interpreted over set-coalgebras with many-valued valuations. The languages are based on many-valued predicate liftings. We provide a characterization theorem for a language generated by a set of such modalities to be expressive for bisimilarity: in addition to the usual condition on the set of predicate liftings being separating, we indicate a sufficient and sometimes also necessary condition on the algebra of truth values which guarantees expressivity. Thus, adapting results of Schroder concerning expressivity of boolean coalgebraic logics to many-valued setting, we generalize results of Metcalfe and Marti, concerning Hennessy-Milner property for many-valued modal logics based on box and diamond.
Keywords
coalgebracoalgebraic logicpredicate liftingmodal logicmany-valued logicexpressivitybisimulationHennessy-Milner property
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Expressivity of Many-Valued Modal Logics, Coalgebraically
Original language description
We apply methods developed to study coalgebraic logic to investigate expressivity of many-valued modal logics which we consider as coalgebraic languages interpreted over set-coalgebras with many-valued valuations. The languages are based on many-valued predicate liftings. We provide a characterization theorem for a language generated by a set of such modalities to be expressive for bisimilarity: in addition to the usual condition on the set of predicate liftings being separating, we indicate a sufficient and sometimes also necessary condition on the algebra of truth values which guarantees expressivity. Thus, adapting results of Schroder concerning expressivity of boolean coalgebraic logics to many-valued setting, we generalize results of Metcalfe and Marti, concerning Hennessy-Milner property for many-valued modal logics based on box and diamond.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Logic, Language, Information, and Computation
ISBN
978-3-662-52920-1
ISSN
0302-9743
e-ISSN
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Number of pages
16
Pages from-to
109-124
Publisher name
Springer
Place of publication
Berlin
Event location
Puebla
Event date
Aug 16, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000389705800008
Basic information
Result type
D - Article in proceedings
CEP
BA - General mathematics
Year of implementation
2016