Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic
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,...
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Springer Verlag
2019
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| LEADER | 06886caa a22007577a 4500 | ||
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| 001 | PAPER-25593 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518205740.0 | ||
| 008 | 190410s2019 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85061488156 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Busaniche, M. | |
| 245 | 1 | 0 | |a Pseudomonadic BL-algebras: an algebraic approach to possibilistic BL-logic |
| 260 | |b Springer Verlag |c 2019 | ||
| 270 | 1 | 0 | |m Cordero, P.; IMAL, CONICET-UNL.Argentina; email: pcordero@santafe-conicet.gov.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Bezhanishvili, N., Pseudomonadic algebras as algebraic models of Doxastic modal logic (2002) Math Log Q, 48, pp. 624-636 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a 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 | ||
| 504 | |a Caicedo, X., Rodriguez, R., Bi-modal Gödel logic over [0,1]-valued Kripke frames (2015) J Log Comput, 25, pp. 37-55 | ||
| 504 | |a 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 | ||
| 504 | |a Cignoli, R., Torrens, A., An algebraic analysis of product logic (2000) Mult Valued Log, 5, pp. 45-65 | ||
| 504 | |a Cignoli, R., D’Ottaviano, I., Mundici, D., (2000) Algebraic foundations of many-valued reasoning, 7. , Kluwer Academic Publishers, Dordrecht: Trends Logic | ||
| 504 | |a Dubois, D., Prade, H., Possibilistic logic: a retrospective and prospective view (2004) Fuzzy Sets Syst, 144, pp. 3-23 | ||
| 504 | |a 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 | ||
| 504 | |a Fitting, M., Many valued modal logics (1991) Fundam Inform, 15, pp. 254-325 | ||
| 504 | |a Fitting, M., Many valued modal logics II (1992) Fundam Inform, 17, pp. 55-73 | ||
| 504 | |a 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 | ||
| 504 | |a Hájek, P., (1998) Metamathematics of fuzzy logic. Trends in logic, , Kluwer, Dordrecht | ||
| 504 | |a Hájek, P., Harmancová, D., Verbrugge, R., A qualitative fuzzy probabilistic logic (1995) J Approx Reason, 12, pp. 1-19 | ||
| 504 | |a Hintikka, J., Knowledge and belief. An introduction to the logic of the two notions (1962) Stud Log, 16, pp. 119-122 | ||
| 520 | 3 | |a 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. |l eng | |
| 536 | |a Detalles de la financiación: 689176 | ||
| 536 | |a Detalles de la financiación: Horizon 2020 | ||
| 536 | |a Detalles de la financiación: CAI+D PIC 50420150100090LI | ||
| 536 | |a Detalles de la financiación: Universidad Nacional del Litoral, UBA-CyT 20020150100002BA, PICT/O N◦ 2016-0215 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas | ||
| 536 | |a Detalles de la financiación: Acknowledgements The authors thank the referees for their comments that helped improve the paper. The authors were funded by the research project PIP 112-20150100412CO, CONICET, Desarrollo de Herramientas Algebraicas y Topológicas para el Estudio de Lóg-icas de la Incertidumbre y la Vaguedad. DHATELIV. M. Busaniche and Penélope Cordero were also funded by the project CAI+D PIC 50420150100090LI, UNL, Métodos algebraico-geométricos en la teoría de la información. Additionally, the author P. Cordero was supported by a CONICET grant during the preparation of the paper. R. O. Rodriguez was also funded by the projects UBA-CyT 20020150100002BA and PICT/O N◦ 2016-0215. The authors have been funded by the Horizon 2020 project of the European Commission 689176–SYSMICS. | ||
| 593 | |a IMAL, CONICET-UNL. FIQ, UNL, Santa Fe, Argentina | ||
| 593 | |a IMAL, CONICET-UNL., Santa Fe, Argentina | ||
| 593 | |a ICC, CONICET-UBA. DC, FCEyN, UBA, Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a BL-ALGEBRAS |
| 690 | 1 | 0 | |a FUZZY POSSIBILISTIC LOGIC |
| 690 | 1 | 0 | |a MODAL ALGEBRAS |
| 690 | 1 | 0 | |a COMPUTER CIRCUITS |
| 690 | 1 | 0 | |a ALGEBRAIC APPROACHES |
| 690 | 1 | 0 | |a APPROXIMATE REASONING |
| 690 | 1 | 0 | |a BL-ALGEBRA |
| 690 | 1 | 0 | |a BL-LOGIC |
| 690 | 1 | 0 | |a EUCLIDEAN |
| 690 | 1 | 0 | |a POSSIBILISTIC |
| 690 | 1 | 0 | |a POSSIBILISTIC LOGIC |
| 690 | 1 | 0 | |a PROPOSITIONAL LOGIC |
| 690 | 1 | 0 | |a FUZZY LOGIC |
| 650 | 1 | 7 | |2 spines |a ALGEBRA |
| 700 | 1 | |a Cordero, P. | |
| 700 | 1 | |a Rodriguez, R.O. | |
| 773 | 0 | |d Springer Verlag, 2019 |g v. 23 |h pp. 2199-2212 |k n. 7 |p Soft Comput. |x 14327643 |t Soft Computing | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s00500-019-03810-0 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_14327643_v23_n7_p2199_Busaniche |y Handle |
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