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Observations on the monoidal t-norm logic. (English) Zbl 1012.03035
The paper is concerned with the properties of some nonclassical logics and their relations, especially to Łukasiewicz logic, Gödel logic, and the monoidal t-norm-based logic. Their relations become stronger if some axioms (the double negation axiom, the idempotence axiom of conjunction and two further specific axioms) are added to them. The main results deal mainly with the monoidal t-norm-based logic and its Archimedian property.

##### MSC:
 03B52 Fuzzy logic; logic of vagueness 03B50 Many-valued logic
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##### References:
 [1] Cignoli, R.; Esteva, F.; Godo, L.; Montagna, F., On a class of left-continuous t-norms, Fuzzy sets and systems, 131, 283-296, (2002) · Zbl 1012.03032 [2] Cintula, P., About axiomatic systems for product logic, Soft comput., 5, 243-244, (2001) · Zbl 0987.03022 [3] F. Esteva, J. Gispert, L. Godo, F. Montagna, On the rational and standard completeness of some axiomatic extensions of the monoidal t-norm logic, Studia Logica, to appear. · Zbl 1011.03015 [4] Esteva, F.; Godo, L., Monoidal t-norms based logictowards a logic for left-continuous t-norms, Fuzzy sets and systems, 124, 271-288, (2001) · Zbl 0994.03017 [5] Flondor, P.; Georgescu, G.; Iorgulescu, A., Pseudo-t-norms and pseudo-BL-algebras, Soft comput., 5, 355-371, (2001) · Zbl 0995.03048 [6] Fodor, J.C., Contrapositive symmetry of fuzzy implications, Fuzzy sets and systems, 69, 141-156, (1995) · Zbl 0845.03007 [7] Fuchs, L., Partially ordered algebraic structures, (1963), Pergamon Press Oxford · Zbl 0137.02001 [8] Gottwald, S.; Jenei, S., A new axiomatization for involutive monoidal t-norm based logic, Fuzzy sets and systems, 124, 303-306, (2001) · Zbl 0998.03024 [9] Hájek, P., Metamathematics of fuzzy logic, (1998), Kluwer Academic Publishers Dordrecht · Zbl 0937.03030 [10] Jenei, S., On Archimedean triangular norms, Fuzzy sets and systems, 99, 179-186, (1998) · Zbl 0938.03083 [11] Jenei, S., New family of triangular norms via contrapositive symmetrization of residuated implications, Fuzzy sets and systems, 110, 117-174, (2000) · Zbl 0941.03059 [12] S. Jenei, Structure of Girard monoids on [0,1], in: Klement et al. (Eds.), Topological and Algebraic Structures in Fuzzy Sets, Kluwer Academic Publishers, Dordrecht, to appear. · Zbl 1036.03035 [13] S. Jenei, F. Montagna, A proof of standard completeness of Esteva and Godo’s logic MTL, Studia Logica, to appear. · Zbl 0997.03027 [14] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, (2000), Kluwer Academic Publishers Dordrecht · Zbl 0972.03002 [15] Kolesárová, A., A note on Archimedean triangular norms, Busefal, 80, 57-60, (1999)
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