On the scope of some formulas defining additive connectives in fuzzy logics

Fuzzy Sets and Systems

Volumn 154, Issue 1, 2005, Pages 56-75

  García Cerdaña, Àngel ^a,b   Noguera, Carles ^b   Esteva, Francesc ^b  

^a ARTIFICIAL INTELLIGENCE RESEARCH INSTITUTE IIIA CSIC   (Spain)

^b UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Additive connectives; IMTL algebras; Involutive left continuous t norms; Left continuous t norms; MTL algebras; Negation functions; Nilpotent minimum t norm; NM algebras; Non classical logics; Residuated fuzzy many valued logics; Residuated lattices

Indexed keywords

BOOLEAN ALGEBRA; COMPUTATIONAL METHODS; FUNCTIONS; LINEAR ALGEBRA; LOGIC PROGRAMMING;

ADDITIVE CONNECTIVES; IMTL-ALGEBRAS; INVOLUTIVE LEFT-CONTINUOUS T-NORMS; LEFT-CONTINUOUS T-NORMS; NEGATION FUNCTIONS; NILPOTENT MINIMUM T-NORMS; NM-ALGEBRAS; NON-CLASSICAL LOGICS; RESIDUATED FUZZY MANY-VALUED LOGICS; RESIDUATED LATTICES;

FUZZY SETS;

EID: 19044375223     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2005.01.004     Document Type: Article

References (24)

1. W.J. Blok, and D. Pigozzi Algebraizable logics Mem. Amer. Math. Soc. 396 1989 77
2. S. Burris, and H.P. Sankappanavar A Course in Universal Algebra 1981 Springer New York
3. R. Cignoli, F. Esteva, L. Godo, and F. Montagna On a class of left-continuous t-norms Fuzzy Sets and Systems 131 2002 283 296
4. R. Cignoli, F. Esteva, L. Godo, and A. Torrens Basic fuzzy logic is the logic of continuous t-norms and their residua Soft Computing 4 2000 106 112
5. F. Esteva, and L. Godo Monoidal t-norm based logic towards a logic for left-continuous t-norms Fuzzy Sets and Systems 124 2001 271 288
6. F. Esteva, A. García-Cerdaña, C. Noguera, On definability of maximum in left-continuous t-norms, Proc. of EUSFLAT 2003, pp. 609-613.
7. F. Esteva, L. Godo, and A. García-Cerdaña On the hierarchy of t-norm based residuated fuzzy logics M. Fitting E. Orlowska Beyond Two Theory and Applications of Multiple-Valued Logic 2003 Springer 251 272
8. F. Esteva, J. Gispert, L. Godo, and F. Montagna On the standard and rational completeness of some axiomatic extensions of monoidal t-norm based logic Studia Logica 71 2002 199 226
9. J. Fodor, Nilpotent minimum and related connectives for fuzzy logic, Proc. of FUZZ-IEEE'95, 1995, pp. 2077-2082.
10. A. García-Cerdaña, C. Noguera, F. Esteva, On definability of additive connectives in fuzzy logics, Proc. of IPMU 2004, pp. 485-492.
11. J.Y. Girard Linear logic Theoretical Computer Science 50 1987 1 102
12. S. Gottwald, A Treatise on Many-valued Logics, Studies in Logic and Computation 9, Research Studies Press Ltd., Baldock, UK, 2001.
13. S. Gottwald, A. García-Cerdaña, and F. Bou Axiomatizing monoidal logic - a correction J. Multiple-valued Logic and Soft Computing 9 2003 427 433
14. P. Hájek, Metamathematics of fuzzy logic, Trends in Logic, vol. 4, Kluwer, 1998.
15. U. Höhle Commutative, residuated l-monoids U. Höhle E.P. Klement Non-Classical Logics and Their Applications to Fuzzy Subsets 1995 Kluwer Academic Publishers Dordrecht 55 106
16. S. Jenei New family of triangular norms via contrapositive symmetrization of residuated implications Fuzzy Sets and Systems 110 1999 157 174
17. S. Jenei A note on the ordinal sum theorem and its consequence for the construction of triangular norms Fuzzy Sets and Systems 126 2002 199 205
18. S. Jenei A characterization theorem on the rotation construction for triangular norms Fuzzy Sets and Systems 136 2003 283 289
19. S. Jenei, and F. Montagna A proof of standard completeness for Esteva and Godo's logic MTL Studia Logica 70 2002 183 192
20. H. Ono, Logic without contraction rule and residuated lattices. To appear in: E. Mares (Ed.), For the Festschrift of Prof. R.K. Meyer.
21. E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica, vol. I, 1 (1979) 47-60. Also in: S. Barro et al. (Eds.), Advances in Fuzzy Logic Public. Univ. S. de Compostela (1998) 31-45.
22. E. Trillas, Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica, vol. I, 1 (1979) 47-60. Also in: S. Barro et al. (Eds.), Advances in Fuzzy Logic Public. Univ. S. de Compostela (1998) 31-45.
23. S.M. Wang, B.S. Wang, and G.J. Wang A triangular-norm-based propositional fuzzy logic Fuzzy Sets and Systems 136 2003 55 77
24. S.M. Wang, B.S. Wang, and D.W. Pei A fuzzy logic for an ordinal sum t-norm Fuzzy Sets and Systems 149 2005 297 307