Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)

Fuzzy Sets and Systems

Volumn 159, Issue 22, 2008, Pages 2970-2982

  Zhou, Hongjun ^a   Wang, Guojun ^a,b  

^a SHAANXI NORMAL UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Boolean theory; Cantor space; Finite separation property; Formal deductive system L*; Maximally consistent theory; Nilpotent minimum logic; Non classical logics; R0 algebra; Three valued ukasiewicz theory

Indexed keywords

BOOLEAN THEORY; CANTOR SPACE; FINITE SEPARATION PROPERTY; FORMAL DEDUCTIVE SYSTEM L*; MAXIMALLY CONSISTENT THEORY; NILPOTENT MINIMUM LOGIC; NON-CLASSICAL LOGICS; R0-ALGEBRA;

ARTIFICIAL INTELLIGENCE;

EID: 51549116272     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2008.04.005     Document Type: Article

References (41)

1. Aguzzoli S., and Gerla B. Normal forms and free algebras for some extensions of MTL. Fuzzy Sets and Systems 159 (2008) 1131-1152
2. Barnes D.W., and Mack J.M. An Algebraic Introduction to Mathematical Logic (1975), Springer, New York
3. Busaniche M. Free nilpotent minimum algebras. Math. Logic Quart. 52 3 (2006) 219-236
4. Cignoli R., D'Ottaviano I.M.L., and Mundici D. Algebraic Foundations of Many-valued Reasoning (2000), Kluwer Academic Publishers, Dordrecht
5. Elkan C. The paradoxical success of fuzzy logic. IEEE Expert 9 4 (1994) 3-8
6. Esteva F., Gispert J., Godo L., and Montagna F. On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm based logic. Studia Logica 71 (2002) 199-226
7. Esteva F., and Godo L. Monoidal t-norm based logic. towards a logic for left-continuous t-norms. Fuzzy Sets and Systems 124 (2001) 271-288
8. Fodor J. Nilpotent minimum and related connectives for fuzzy logic. Proc. FUZZ-IEEE'95 (1995) 2077-2082
9. Gottwald S. A Treatise on Many-valued Logics, Studies in Logic and Computation (2001), Research Studies Press, Baldock
10. Gottwald S., and Novák V. On the consistency of fuzzy theories. Proc. Seventh IFSA World Congress (1997), Academia, Prague 168-171
11. Hájek P. Metamathematics of Fuzzy Logic (1998), Kluwer Academic Publishers, Dordrecht
12. Hájek P., Godo L., and Esteva F. A complete many-valued logic with product-conjunction. Arch. Math. Logic 35 (1996) 191-208
13. 0-algebras. J. Shaanxi Normal Univ. 32 1 (2004) 25-28 (Natural Science edition)
14. *. J. Shaanxi Normal Univ. 33 2 (2005) 9-12 (Natural Science edition)
15. Kelley J.L. General Topology (1955), Springer, New York
16. S. Koppelberg, Handbook of Boolean Algebras, Vol. 1, North-Holland, Amsterdam, 1989.
17. Liu H.W., and Wang G.J. Unified forms of fully implicational restriction methods for fuzzy reasoning. Inform. Sci. 177 (2007) 956-966
18. Mill J.V. Infinite-Dimensional Topology (1988), North-Holland, Amsterdam
19. Munkres J.R. Topology. second ed. (2004), China Machine Press, Beijing
20. Noguera C., Esteva F., and Gispert J. On some varieties of MTL-algebras. Logic J. IGPL 13 (2005) 443-466
21. Novák V., Perfilieva I., and Močkoř J. Mathematical Principles of Fuzzy Logic (1999), Kluwer Academic Publishers, Boston
22. *. Fuzzy Systems Math. 15 (2001) 34-39
23. Pei D.W. On equivalent forms of fuzzy logic systems NM and IMTL. Fuzzy Sets and Systems 138 (2003) 187-195
24. *. Sci. China F 45 (2002) 40-50
25. Song S.J., Feng C.B., and Lee E.S. Triple I method of fuzzy reasoning. Comput. Math. Appl. 44 (2002) 1567-1579
26. Turunen E. Mathematics Behind Fuzzy Logic (1999), Physica-Verlag, Heidelberg
27. Wang G.J. Fuzzy logic and fuzzy reasoning. Proc. Seventh National Many-valued and Fuzzy Logic Academic Conf. Xi'an (1996) 82-96
28. Wang G.J. A formal deductive system for fuzzy propositional calculus. Chinese Sci. Bull. 42 (1997) 1521-1526
29. Wang G.J. On the logic foundation of fuzzy reasoning. Inform. Sci. 117 (1999) 47-88
30. G.J. Wang, The full implicational triple I method of fuzzy reasoning, Sci. China E (1999) 44-53.
31. Wang G.J. Theory of Non-classical Mathematical Logic and Approximate Reasoning (2000), Science in China Press, Beijing (in Chinese)
32. Wang G.J. Formalized theory of general fuzzy reasoning. Inform. Sci. 160 (2004) 251-266
33. Wang G.J. Introduction to Mathematical Logic and Resolution Principle. second ed. (2006), Science in China Press, Beijing (in Chinese)
34. Wang G.J., and Fu L. Unified forms of triple I method. Comput. Math. Appl. 49 (2005) 923-932
35. Wang S.M., Wang B.S., and Wang G.J. A triangular norm-based propositional fuzzy logic. Fuzzy Sets and Systems 136 (2003) 55-70
36. Wang S.M., Wang B.S., and Wang X.Y. A characterization of truth-functions in the nilpotent minimum logic. Fuzzy Sets and Systems 145 (2004) 253-266
37. Wang S.M., and Wang M.Y. Undefinability of min-conjunction in MTL. Fuzzy Sets and Systems 157 (2006) 670-676
38. Zadeh L.A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Systems Man Cybernet. 3 (1974) 28-44
39. Zhou H.J., and Wang G.J. A new theory consistency index based on deduction theorem in several logic systems. Fuzzy Sets and Systems 157 (2006) 427-443
40. Zhou H.J., and Wang G.J. Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems. Fuzzy Sets and Systems 157 (2006) 2058-2073
41. * (NM-logic) and Cantor space. Fuzzy Sets and Systems 158 (2007) 2591-2604