On triangular norm based axiomatic extensions of the weak nilpotent minimum logic

Mathematical Logic Quarterly

Volumn 54, Issue 4, 2008, Pages 387-409

  Noguera, Carles ^a   Esteva, Francesc ^b   Gispert, Joan ^c  

^a UNIVERSITY OF LLEIDA   (Spain)

^b ARTIFICIAL INTELLIGENCE RESEARCH INSTITUTE IIIA CSIC   (Spain)

^c UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Algebraic logic; Fuzzy logic; Left continuous t norm; Mathematical fuzzy logic; Monoidal triangular norm based logic; MTL algebra; Nilpotent minimum logic; Non classical logic; Residuated lattice; Substructural logic; Variety; Weak nilpotent minimum logic

Indexed keywords

EID: 55449101926     PISSN: 09425616     EISSN: 15213870     Source Type: Journal    
DOI: 10.1002/malq.200710054     Document Type: Article

References (27)

1. W. J. Blok and D. Pigozzi, On the structure of varieties with equationally definable principal congruences I. Algebra Universalis 15, 195-227 (1982).
2. W. J. Blok and D. Pigozzi, Algebraizable Logics. Mem. Amer. Math. Soc. 396, vol. 77 (1989).
3. W. J. Blok and D. Pigozzi, Abstract algebraic logic and the deduction theorem. To appear in the Bulletin of Symbolic Logic.
4. W. J. Blok and C. J. Van Alten, The finite embeddability property for residuated lattices, pocrims and BCK-algebras. Algebra Universalis 48, 253-271 (2002).
5. S. Burris and H. P. Sankappanavar, A Course in Universal Algebra (Springer-Verlag, 1981).
6. A. Ciabattoni, F. Esteva, and L. Godo, T-norm based logics with n-contraction. Neural Network World 5, 441-452 (2002).
7. P. Cintula, F. Esteva, J. Gispert, L. Godo, F. Montagna, and C. Noguera, Distinguished algebraic semantics for t-norm based fuzzy logics: methods and algebraic equivalencies. Submitted (2007).
8. M. Dummett, A propositional calculus with denumerable matrix. J. Symbolic Logic 24, 97-106 (1959).
9. F. Esteva and X. Domingo, Sobre negaciones fuertes y débiles en [0, 1]. Stochastica 4, 141-166 (1980).
10. F. Esteva and L. Godo, Monoidal t-norm based logic: Towards a logic for left-continuous t-norms. Fuzzy Sets and Systems 124, 271-288 (2001).
11. F. Esteva, L. Godo, and C. Noguera, On expansions of t-norm based logics with truth-constants. To appear in the book "Fuzzy Logics and Related Structures" (S. Gottwald, P. Hájek, U. Höhle, and E. P. Klement, eds.), 2007.
12. J. Fodor, Nilpotent minimum and related connectives for fuzzy logic. In: Proceedings of FUZZ-IEEE'95, 1995, pp. 2077-2082.
13. A. García-Cerdaña, C. Noguera, and F. Esteva, On the scope of some formulas defining additive connectives in fuzzy logics. Fuzzy Sets and Systems 154, 56-75 (2005).
14. J. Gispert, Axiomatic extensions of the nilpotent minimum logic. Reports on Mathematical Logic 37, 113-123 (2003).
15. K. Gödel, Zum intuitionistischen Aussagenkalkül. Anzeiger Akademie der Wissenschaften Wien, Math.-naturwiss. Klasse 69, 65-66 (1932).
16. S. Gottwald, A Treatise on Many-Valued Logics. Studies in Logic and Computation 9 (Research Studies Press Ltd., 2001).
17. P. Hájek, Metamathematics of Fuzzy Logic. Trends in Logic 4 (Kluwer, 1998).
18. U. Höhle, Commutative, residuated l-monoids. In: Non-Classical Logics and Their Applications to Fuzzy Subsets (U. Höhle and E. P. Klement, eds.), pp. 55-106 (Kluwer Academic Publishers, 1995).
19. R. Horčík, C. Noguera, and M. Petrík, On n-contractive fuzzy logics. Math. Logic Quart. 53, 268-288 (2007).
20. S. Jenei and F. Montagna, A proof of standard completeness for Esteva and Godo's logic MTL. Studia Logica 70, 183-192 (2002).
21. C. Noguera, Algebraic study of axiomatic extensions of triangular norm based fuzzy logics. Ph. D. dissertation, Universitat de Barcelona, 2006.
22. C. Noguera, F. Esteva, and J. Gispert, Perfect and bipartite IMTL-algebras and disconnected rotations of prelinear semihoops. Arch. Math. Logic 44, 869-886 (2005).
23. C. Noguera, F. Esteva, and J. Gispert, On some varieties of MTL-algebras. Logic J. IGPL 13, 443-466 (2005).
24. C. Noguera, F. Esteva, and J. Gispert, On varieties generated by weak nilpotent minimum t-norms. In: Proceedings of Fourth EUSFLAT, Barcelona, 2005, pp. 866-871.
25. D. Pei, The equivalent forms of fuzzy logic systems NM and IMTL. Fuzzy Sets and Systems 138, 187-195 (2003).
26. E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica 3, 47-60 (1979).
27. English translation in "Advances in Fuzzy Logic" (S. Barro, A. Bugarin, and A. Sobrino, eds.), Public. Univ. Santiago de Compostela (Spain), pp. 31-45.