Abstract
In this paper we develop the non-commutative product logic psΠL as the non-commutative analogue of the product logic ΠL introduced by Hájek, Godo and Esteva [10]. The investigation of this logical system is an open problem in Hájek [9]. We also introduce a probabilistic logic based on the non-commutative product logic capable to reason about the probability of fuzzy events.
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References
Cignoli, R., Torrens, A.: An algebraic analysis of product logic. Multiple-Valued Logic 5, 45–65 (2000)
DiNola, A., Georgescu, G., Iorgulescu, A.: Pseudo-BL algebras -part II. Multiple-Valued Logic 8(5-6), 717–750 (2002)
Dvurečenskij, A., Rachůnek, J., Šalounová, D.: State operators on generalizations of fuzzy structures. Fuzzy Sets and Systems 187(1), 58–76 (2012)
Flaminio, T., Godo, L.: A logic for reasoning about the probability of fuzzy events. Fuzzy Sets and Systems 158, 625–638 (2007)
Flaminio, T., Montagna, F.: MV-algebras with internal states and probabilistic fuzzy logics. International Journal of Approximate Reasoning 50, 138–152 (2009)
Georgescu, G.: Bosbach states on fuzzy structures. Soft Computing 8, 217–230 (2004)
Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic, vol. 4. Kluwer, Dordrecht (1998)
Hájek, P.: Fuzzy logics with non-commutative conjunctions. Journal of Logic and Computation 13, 469–479 (2003)
Hájek, P.: Observations on non-commutative fuzzy logic. Soft Computing 8, 38–43 (2003)
Hájek, P., Godo, L., Esteva, F.: A complete many-valued logic with product-conjunction. Arch. Math. Logic 35(3), 191–208 (1996)
Leuştean, I.: Non-commutative Łukasiewicz propositional logic. Arch. Math. Logic 45(2), 191–213 (2006)
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Diaconescu, D. (2012). Non-commutative Product Logic and Probability of Fuzzy Events. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_22
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DOI: https://doi.org/10.1007/978-3-642-31715-6_22
Publisher Name: Springer, Berlin, Heidelberg
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