NMŁ, a schematic extension of F.Esteva and L.Godo's logic MTL

Fuzzy Sets and Systems

Volumn 149, Issue 2, 2005, Pages 285-295

  Wang, San Min ^a,c   Wang, Bao Shu ^a   Ren, Fang ^b  

^a XIDIAN UNIVERSITY   (China)

^b SHAANXI NORMAL UNIVERSITY   (China)

^c NANCHANG UNIVERSITY   (China)

Author keywords

ukasiewicz system; Left continuous t norm; MTL system; NM system; NM system; Non classical logics

Indexed keywords

DIFFERENTIAL EQUATIONS; METRIC SYSTEM; NONLINEAR SYSTEMS; SEMANTICS; SET THEORY; THEOREM PROVING;

LEFT-CONTINUOUS T-NORM; LUKASIEWICZ SYSTEMS; MTL SYSTEMS; NM SYSTEMS; NML SYSTEMS; NON-CLASSICAL LOGICS;

FUZZY SETS;

EID: 9644289345     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2003.12.005     Document Type: Article

References (15)

1. R. Cignoli, F. Esteva, L. Godo, A. Torrens, Basic fuzzy logic is the logic of continuous t-norms and their residua, Soft Comput. 4 (2000) 106-112.
2. F. Esteva, L. Godo, Monoidal t-norm based logic; towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124 (2001) 271-288.
3. F. Esteva, L. Godo, J. Gispert, F. Montagna, On the standard and rational completeness of some axiomatic extensions of the monoidal T-norm logic, Studia Logica 71 (2002) 199-226.
4. J.C. Fodor, Contrapositive symmetry of fuzzy implications, Fuzzy Sets and Systems 69 (1995) 141-156.
5. P. Hájek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
6. P. Hájek, Basic fuzzy logic and BL-algebras, Soft Comput. 2 (1998) 124-128.
7. P. Hájek, Observations on the Monoidal t-norm Logic, Fuzzy Sets and Systems 132 (2002) 107-112.
8. S. Jenei, A new family of triangular norms via contrapositive symmetrization of residuated implication, Fuzzy Sets and Systems 110 (2) (2000) 157-174.
9. S. Jenei, F. Montagna, A proof of standard completeness of Esteva and Godo's monoidal logic MTL, Studia Logica 70 (2) (2002) 184-192.
10. E.P. Klement, M. Navara, A survey on different triangular norm-based fuzzy logics, Fuzzy Sets and Systems 101 (2) (1999) 241-251.
11. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000.
12. D. Pei, The equivalent forms of fuzzy logic systems NM and IMTL, Fuzzy Sets and Systems 138 (1) (2003) 187-195.
13. A. Rose, J.B. Rosser, Fragment of many-valued statement calculi, Trans. Amer. Math. Soc. 87 (1958) 1-53.
14. G.-J. Wang, A formal deductive system for fuzzy propositional calculus, Chinese Sci. Bull. 42 (1997) 1521-1526.
15. S.-M. Wang, B.-S. Wang, G.-J. Wang, A triangular norm-based propositional fuzzy logic, Fuzzy Sets and Systems 136 (1) (2003) 55-70.