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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2009
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou http://hdl.handle.net/20.500.12110/paper_97898995_v_n_p1541_Bou |
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paper:paper_97898995_v_n_p1541_Bou |
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paper:paper_97898995_v_n_p1541_Bou2023-06-08T16:39:17Z Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou 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 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. |
| 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 |
| publishDate |
2009 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou http://hdl.handle.net/20.500.12110/paper_97898995_v_n_p1541_Bou |
| _version_ |
1769175845680709632 |