Abstract:
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.
Registro:
| Documento: |
Conferencia
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| Título: | Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations |
| Autor: | Bou, F.; Esteva, F.; Godo, L.; Rodríguez, R. |
| Ciudad: | Lisbon |
| Filiación: | Institut d'Investigació en Intelligència Artificial, IIIA, CSIC, Campus UAB, 08193 Bellaterra, Spain
Dpto. de Computación, Universidad Buenos Aires, 1428 Buenos Aires, Argentina
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| Palabras clave: | 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 |
| Año: | 2009
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| Página de inicio: | 1541
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| Página de fin: | 1546
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| Título revista: | Joint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009
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| Título revista abreviado: | Int. Fuzzy Syst. Assoc. World Congr. Eur. Soc. Fuzzy Logic Technol. Conf., IFSA-EUSFLAT - Proc.
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou |
Referencias:
- Bou, F., Esteva, F., Godo, L., Rodríguez, R., (2008) On the Minimum Many-valued Modal Logic Over a Finite Residuated Lattice, , http://arxiv.org/abs/0811.2107, Submitted
- Zadeh, L.A., Similarity relations and fuzzy orderings (1971) Information Sciences, 3, pp. 177-200
- Höhle, U., Commutative, residuated l-monoids (1995) Non-classical Logics and their Applications to Fuzzy Subsets (Linz, 1992), Volume 32 of Theory Decis. Lib. Ser. B Math. Statist. Methods, pp. 53-106. , U. Höhle and E. P. Klement, editors Kluwer Acad. Publ., Dordrecht
- Jipsen, P., Tsinakis, C., A survey of residuated lattices (2002) Ordered Algebraic Structures, pp. 19-56. , J. Martinez, editor Kluwer Academic Publishers, Dordrecht
- Ono, H., Substructural logics and residuated lattices - An introduction (2003) 50 Years of Studia Logica, Volume 21 of Trends in Logic - Studia Logica Library, pp. 193-228. , V. F. Hendricks and J. Malinowski, editors Dordrecht
- Esteva, F., Godo, L., Monoidal t-norm based logic: Towards a logic for left-continuous t-norms (2001) Fuzzy Sets and Systems, 124, pp. 271-288
- Hájek, P., (1998) Metamathematics of Fuzzy Logic, Volume 4 of Trends in Logic - Studia Logica Library, , Kluwer Academic Publishers, Dordrecht
- Cignoli, R., D'Ottaviano, I.M.L., Mundici, D., (2000) Algebraic Foundations of Many-valued Reasoning, Volume 7 of Trends in Logic - Studia Logica Library, , Kluwer Academic Publishers, Dordrecht
- Blackburn, P., Van Benthem, J.F.A.K., Wolter, F., (2006) Handbook of Modal Logic, Volume 3 (Studies in Logic and Practical Reasoning), , Elsevier Science Inc., New York, NY, USA
Citas:
---------- APA ----------
Bou, F., Esteva, F., Godo, L. & Rodríguez, R.
(2009)
. Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations. Joint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009, 1541-1546.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou [ ]
---------- CHICAGO ----------
Bou, F., Esteva, F., Godo, L., Rodríguez, R.
"Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations"
. Joint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009
(2009) : 1541-1546.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou [ ]
---------- MLA ----------
Bou, F., Esteva, F., Godo, L., Rodríguez, R.
"Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations"
. Joint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009, 2009, pp. 1541-1546.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou [ ]
---------- VANCOUVER ----------
Bou, F., Esteva, F., Godo, L., Rodríguez, R. Characterizing fuzzy modal semantics by fuzzy multimodal systems with crisp accessibility relations. Int. Fuzzy Syst. Assoc. World Congr. Eur. Soc. Fuzzy Logic Technol. Conf., IFSA-EUSFLAT - Proc. 2009:1541-1546.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97898995_v_n_p1541_Bou [ ]
