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Abstract:

Fuzzy possibilistic logic is an important formalism for approximate reasoning. It extends the well-known basic propositional logic BL, introduced by Hájek, by offering the ability to reason about possibility and necessity of fuzzy propositions. We consider an algebraic approach to study this logic, introducing Pseudomonadic BL-algebras. These algebras turn to be a generalization of both Pseudomonadic algebras introduced by Bezhanishvili (Math Log Q 48:624–636, 2002) and serial, Euclidean and transitive Bimodal Gödel algebras proposed by Caicedo and Rodriguez (J Log Comput 25:37–55, 2015). We present the connection between this class of algebras and possibilistic BL-frames, as a first step to solve an open problem proposed by Hájek (Metamathematics of fuzzy logic. Trends in logic, Kluwer, Dordrecht, 1998, Chap. 8, Sect. 3). © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

Registro:

Documento: Artículo
Título:Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic
Autor:Busaniche, M.; Cordero, P.; Rodriguez, R.O.
Filiación:IMAL, CONICET-UNL. FIQ, UNL, Santa Fe, Argentina
IMAL, CONICET-UNL., Santa Fe, Argentina
ICC, CONICET-UBA. DC, FCEyN, UBA, Buenos Aires, Argentina
Palabras clave:BL-algebras; Fuzzy possibilistic logic; Modal algebras; Algebra; Computer circuits; Algebraic approaches; Approximate reasoning; BL-algebra; BL-logic; Euclidean; Possibilistic; Possibilistic logic; Propositional logic; Fuzzy logic
Año:2019
Volumen:23
Número:7
Página de inicio:2199
Página de fin:2212
DOI: http://dx.doi.org/10.1007/s00500-019-03810-0
Título revista:Soft Computing
Título revista abreviado:Soft Comput.
ISSN:14327643
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14327643_v23_n7_p2199_Busaniche

Referencias:

  • Bezhanishvili, N., Pseudomonadic algebras as algebraic models of Doxastic modal logic (2002) Math Log Q, 48, pp. 624-636
  • Bou, F., Esteva, F., Godo, L., Rodriguez, R., On the minimum many-valued modal logic over a finite residuated lattice (2011) J Log Comput, 21, pp. 739-790
  • Bou, F., Esteva, F., Godo, L., Rodriguez, R., Possibilistic semantics for a modal K D 45 extension of Gödel fuzzy logic (2016) IPMU 2016, Eindhoven, the Netherlands, 20–24 June 2016, Proceedings, Part II. Communications in Computer and Information Science, 611. , Springer
  • Busaniche, M., Montagna, F., Hájek’s logic BL and BL-algebras (2011) Handbook of mathematical fuzzy logic, volume 1 of studies in logic, mathematical logic and foundations, 1, pp. 355-447. , College Publications, London
  • Caicedo, X., Rodriguez, R., Bi-modal Gödel logic over [0,1]-valued Kripke frames (2015) J Log Comput, 25, pp. 37-55
  • Castaño, D., Cimadamore, C., Díaz Varela, P., Rueda, L., Monadic BL-algebras: the equivalent algebraic semantics of Hájek’s monadic fuzzy logic (2017) Fuzzy Sets Syst, 320, pp. 40-59
  • Cignoli, R., Torrens, A., An algebraic analysis of product logic (2000) Mult Valued Log, 5, pp. 45-65
  • Cignoli, R., D’Ottaviano, I., Mundici, D., (2000) Algebraic foundations of many-valued reasoning, 7. , Kluwer Academic Publishers, Dordrecht: Trends Logic
  • Dubois, D., Prade, H., Possibilistic logic: a retrospective and prospective view (2004) Fuzzy Sets Syst, 144, pp. 3-23
  • Dubois, D., Land, J., Prade, H., Possibilistic logic (1994) Handbook of logic in artificial intelligence and logic programing, non-monotonic reasoning and uncertain reasoning, 3, pp. 439-513. , Gabbay, (ed), Oxford University Press, Oxford
  • Fitting, M., Many valued modal logics (1991) Fundam Inform, 15, pp. 254-325
  • Fitting, M., Many valued modal logics II (1992) Fundam Inform, 17, pp. 55-73
  • Galatos, N., Jipsen, P., Kowalski, T., Ono, H., (2007) Residuated lattices: an algebraic glimpse at substructural logics, volume 151 of studies in logic and the foundation of mathematics, , Elsevier, Amsterdam
  • Hájek, P., (1998) Metamathematics of fuzzy logic. Trends in logic, , Kluwer, Dordrecht
  • Hájek, P., Harmancová, D., Verbrugge, R., A qualitative fuzzy probabilistic logic (1995) J Approx Reason, 12, pp. 1-19
  • Hintikka, J., Knowledge and belief. An introduction to the logic of the two notions (1962) Stud Log, 16, pp. 119-122

Citas:

---------- APA ----------
Busaniche, M., Cordero, P. & Rodriguez, R.O. (2019) . Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic. Soft Computing, 23(7), 2199-2212.
http://dx.doi.org/10.1007/s00500-019-03810-0
---------- CHICAGO ----------
Busaniche, M., Cordero, P., Rodriguez, R.O. "Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic" . Soft Computing 23, no. 7 (2019) : 2199-2212.
http://dx.doi.org/10.1007/s00500-019-03810-0
---------- MLA ----------
Busaniche, M., Cordero, P., Rodriguez, R.O. "Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic" . Soft Computing, vol. 23, no. 7, 2019, pp. 2199-2212.
http://dx.doi.org/10.1007/s00500-019-03810-0
---------- VANCOUVER ----------
Busaniche, M., Cordero, P., Rodriguez, R.O. Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic. Soft Comput. 2019;23(7):2199-2212.
http://dx.doi.org/10.1007/s00500-019-03810-0