Consistency degrees of theories and methods of graded reasoning in n-valued R0-logic (NM-logic)

International Journal of Approximate Reasoning

Volumn 43, Issue 2, 2006, Pages 117-132

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

^a SHAANXI NORMAL UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

Completeness theorem; Consistency degree; Deduction theorem; Degree of entailment; Graded reasoning; Limit theorem; R0 logic; Truth degree

Indexed keywords

FORMAL LOGIC; GAMMA RAYS; NUMERICAL METHODS;

COMPLETENESS THEOREM; CONSISTENCY DEGREE; DEDUCTION THEOREM; DEGREE OF ENTAILMENT; GRADED REASONING; LIMIT THEOREM; TRUTH DEGREE;

THEOREM PROVING;

EID: 33748574567     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2006.03.001     Document Type: Article

References (21)

1. Esteva F., and Godo L. Monoidal t-norm based logic: towards a logic of left-continuous t-norms. Fuzzy Sets Syst. 124 (2001) 271-288
2. Gottwald S. A Treatise on Many-Valued Logics, Studies in Logic and Computation (2001), Research Studies Press, Baldock
3. Gottwald S., and Novák V. On the consistency of fuzzy theories. Proc. of 7th IFSA World Congress (1997), Academi, Prague 168-171
4. Hájek P. Metamathematics of Fuzzy Logic (1998), Kluwer Academic Publishers, Dordrect
5. Halmos P.R. Measure Theory (1974), Springer-Verlag, New York
6. 0 logic. Int. J. Intelligent Syst. 199 (2004) 491-497
7. Novák V., Perfilieva I., and Močkoř J. Mathematical Principles of Fuzzy Logic (1999), Kluwer Academic Publishers, Boston
8. Pei D.W. On equivalent forms of fuzzy logic systems NM and IMTL. Fuzzy Sets Syst. 138 (2003) 187-195
9. *. Fuzzy Syst. Math. 15 (2001) 39 (in Chinese)
10. *. Sci. China F 45 (2002) 40-50
11. *. Appl. Math. J. Chinese Univ. Ser. A 16 3 (2001) 253-262
12. Wang G.J. A formal deductive system for fuzzy propositional calculus. Chinese Sci. Bull. 42 (1997) 1521-1526
13. Wang G.J. Comparison of deduction theorems in diverse logic systems. New Math. Natural Comput. 1 1 (2005) 65-77
14. Wang G.J. Introduction to Mathematical Logic and Resolution Principle (2003), Science in China Press, Beijing (in Chinese)
15. Wang G.J. Theory of truth degrees of formulas in Łukasiewicz n-valued propositional logic and a limit theorem. Sci. China Inform. Sci. E 35 6 (2005) 561-569 (in Chinese)
16. Wang G.J., and Leung Y. Integrated semantics and logic metric spaces. Fuzzy Sets Syst. 136 (2003) 71-91
17. Wang G.J., and Zhang W.X. Consistency degrees of finite theories in Łukasiewicz propositional fuzzy logic. Fuzzy Sets Syst. 149 (2005) 275-284
18. Wang S.M., Wang B.S., and Wang G.J. A triangular-norm-based propositional fuzzy logic. Fuzzy Sets Syst. 136 (2003) 55-70
19. Zhou H.J., and Wang G.J. A new theory consistency index based on deduction theorems in several logic systems. Fuzzy Sets Syst. 157 (2006) 427-443
20. H.J. Zhou, G.J. Wang, Generalized consistency degrees of theories w.r.t. formulas in several standard complete logic systems. Fuzzy Sets and Systems, in press.
21. Zhou X.N., and Wang G.J. Consistency degrees of theories in some systems of propositional fuzzy logic. Fuzzy Sets Syst. 152 (2005) 321-331