Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions

In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic G. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel fr...

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Authors: Rodriguez, Ricardo O., Tuyt, Olim Frits, Esteva, Francesc, Godo, Lluis
Format: article
Publication Date:2022
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/282416
Online Access:http://hdl.handle.net/10261/282416
https://api.elsevier.com/content/abstract/scopus_id/85127727932
Access Level:Open access
Keyword:Epistemic logics
Many-valued modal logics
Possibilistic semantics
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spelling Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic ExtensionsRodriguez, Ricardo O.Tuyt, Olim FritsEsteva, FrancescGodo, LluisEpistemic logicsMany-valued modal logicsPossibilistic semanticsIn this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic G. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames ⟨ W, π⟩ , where W is a non-empty set of worlds and π: W→ [0 , 1] is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames ⟨ W, π⟩ where π satisfies the normalisation condition sup w∈Wπ(w) = 1.Peer reviewedSpringer NatureRodriguez, Ricardo O. [0000-0001-7551-2877]Esteva, Francesc [0000-0003-4466-3298]Godo, Lluis [0000-0002-6929-3126]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202220222022info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://hdl.handle.net/10261/282416https://api.elsevier.com/content/abstract/scopus_id/85127727932reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)InglésStudia LogicaSíinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2824162026-05-22T06:33:51Z
dc.title.none.fl_str_mv Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
title Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
spellingShingle Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
Rodriguez, Ricardo O.
Epistemic logics
Many-valued modal logics
Possibilistic semantics
title_short Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
title_full Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
title_fullStr Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
title_full_unstemmed Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
title_sort Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its Axiomatic Extensions
dc.creator.none.fl_str_mv Rodriguez, Ricardo O.
Tuyt, Olim Frits
Esteva, Francesc
Godo, Lluis
author Rodriguez, Ricardo O.
author_facet Rodriguez, Ricardo O.
Tuyt, Olim Frits
Esteva, Francesc
Godo, Lluis
author_role author
author2 Tuyt, Olim Frits
Esteva, Francesc
Godo, Lluis
author2_role author
author
author
dc.contributor.none.fl_str_mv Rodriguez, Ricardo O. [0000-0001-7551-2877]
Esteva, Francesc [0000-0003-4466-3298]
Godo, Lluis [0000-0002-6929-3126]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Epistemic logics
Many-valued modal logics
Possibilistic semantics
topic Epistemic logics
Many-valued modal logics
Possibilistic semantics
description In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic G. More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames ⟨ W, π⟩ , where W is a non-empty set of worlds and π: W→ [0 , 1] is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames ⟨ W, π⟩ where π satisfies the normalisation condition sup w∈Wπ(w) = 1.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/282416
https://api.elsevier.com/content/abstract/scopus_id/85127727932
url http://hdl.handle.net/10261/282416
https://api.elsevier.com/content/abstract/scopus_id/85127727932
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Studia Logica
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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