Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus...

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Detalles Bibliográficos
Autores principales: Bou, F., Esteva, F., Godo, L., Rodríguez, R.
Formato: CONF
Materias:
Łukasiewicz modal logic
Fuzzy logic
Fuzzy modal logic
Many-valued modal logic
Expressive power
Finite chains
Fuzzy modal
Kripke-style semantics
Modal logic
Multi-modal
Multi-modal logic
Multimodal system
Residuated lattices
Truth values
Fuzzy systems
Semantics
Many valued logics
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_97898995_v_n_p1541_Bou
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_97898995_v_n_p1541_Bou
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spelling todo:paper_97898995_v_n_p1541_Bou2023-10-03T16:45:32Z Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations Bou, F. Esteva, F. Godo, L. Rodríguez, R. Łukasiewicz modal logic Fuzzy logic Fuzzy modal logic Many-valued modal logic Expressive power Finite chains Fuzzy modal Fuzzy modal logic Kripke-style semantics Modal logic Multi-modal Multi-modal logic Multimodal system Residuated lattices Truth values Fuzzy logic Fuzzy systems Semantics Many valued logics In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multimodal logic where the previous necessity operator is replaced with a family, parametrized by truth values different from zero, of necessity operators each one semantically defined using the crisp accessibility relation given by the corresponding cut of the finitely-valued original accessibility relation. This multimodal logic is somehow more appealing than the original modal one because axiom (K) holds for each necessity operator. In this paper we axiomatize this multimodal logic and we prove that, in the case the starting residuated lattice is a finite BL chain, the modal and the multimodal languages have the same expressive power iff this algebra is an MV chain. CONF info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_97898995_v_n_p1541_Bou
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Łukasiewicz modal logic
Fuzzy logic
Fuzzy modal logic
Many-valued modal logic
Expressive power
Finite chains
Fuzzy modal
Fuzzy modal logic
Kripke-style semantics
Modal logic
Multi-modal
Multi-modal logic
Multimodal system
Residuated lattices
Truth values
Fuzzy logic
Fuzzy systems
Semantics
Many valued logics
spellingShingle Łukasiewicz modal logic
Fuzzy logic
Fuzzy modal logic
Many-valued modal logic
Expressive power
Finite chains
Fuzzy modal
Fuzzy modal logic
Kripke-style semantics
Modal logic
Multi-modal
Multi-modal logic
Multimodal system
Residuated lattices
Truth values
Fuzzy logic
Fuzzy systems
Semantics
Many valued logics
Bou, F.
Esteva, F.
Godo, L.
Rodríguez, R.
Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
topic_facet Łukasiewicz modal logic
Fuzzy logic
Fuzzy modal logic
Many-valued modal logic
Expressive power
Finite chains
Fuzzy modal
Fuzzy modal logic
Kripke-style semantics
Modal logic
Multi-modal
Multi-modal logic
Multimodal system
Residuated lattices
Truth values
Fuzzy logic
Fuzzy systems
Semantics
Many valued logics
description In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multimodal logic where the previous necessity operator is replaced with a family, parametrized by truth values different from zero, of necessity operators each one semantically defined using the crisp accessibility relation given by the corresponding cut of the finitely-valued original accessibility relation. This multimodal logic is somehow more appealing than the original modal one because axiom (K) holds for each necessity operator. In this paper we axiomatize this multimodal logic and we prove that, in the case the starting residuated lattice is a finite BL chain, the modal and the multimodal languages have the same expressive power iff this algebra is an MV chain.
format CONF
author Bou, F.
Esteva, F.
Godo, L.
Rodríguez, R.
author_facet Bou, F.
Esteva, F.
Godo, L.
Rodríguez, R.
author_sort Bou, F.
title Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
title_short Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
title_full Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
title_fullStr Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
title_full_unstemmed Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
title_sort characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations
url http://hdl.handle.net/20.500.12110/paper_97898995_v_n_p1541_Bou
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AT estevaf characterizingfuzzymodalsemanticsbyfuzzymultimodalsystemswithcrispaccessibilityrelations
AT godol characterizingfuzzymodalsemanticsbyfuzzymultimodalsystemswithcrispaccessibilityrelations
AT rodriguezr characterizingfuzzymodalsemanticsbyfuzzymultimodalsystemswithcrispaccessibilityrelations
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