The Theory of Membership Degree of Γ-Conclusion in Several n-Valued Logic Systems
Author(s) Jiancheng Zhang
ABSTRACT
Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership degree of formulas A is a consequence of Γ (or Γ-conclusion) in Lukasiewicz n-valued propositional logic systems, Godel n-valued propositional logic system and the R0 n-valued propositional logic systems. The condition and related calculations of formulas A being Γ-conclusion were discussed by extent method. At the same time, some properties of membership degree of formulas A is a Γ-conclusion were given. We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root.

Cite this paper
J. Zhang, "The Theory of Membership Degree of Γ-Conclusion in Several n-Valued Logic Systems," American Journal of Operations Research, Vol. 2 No. 2, 2012, pp. 147-152. doi: 10.4236/ajor.2012.22017.
References
   H. W. Liu and G. J. Wang, “Unified Forms of Fully Implicational Restriction Methods for Fuzzy Reasoning,” Information Sciences, Vol. 177, No. 3, 2007, pp. 956-966. doi:10.1016/j.ins.2006.08.012

   J. Pavelka, “On Fuzzy Logic II-Enriched Residuated Lattices and Semantics of Propositional Calculi,” Zeitschrift für mathematische Logik und Grundlagen der Mathematik, Vol. 25, 2011, pp. 119-134.

   G. J. Wang and H. Wang, “Non-Fuzzy Versions of Fuzzy Reasoning in Classical Logic,” Information Sciences, Vol. 138, No. 1-4, 2011, pp. 211-236. doi:10.1016/S0020-0255(01)00131-1

   G. J. Wang, “On the Logic Foundation of Fuzzy Reasoning,” Information Sciences, Vol. 117, No. 1-2, 1999, pp. 47-88. doi:10.1016/S0020-0255(98)10103-2

   M. S. Ying, “Compactness, the L?wenheim-Skolem Property and the Direct Product of Lattices of Truth Values,” Zeitschrift für mathematische Logik und Grundlagen der Mathematik, Vol. 38, 1992, pp. 521-524.

   F. Esteva and L. Godo, “Monoidal t-Norm Based Logic: Towards a Logic for Left-Continuous t-Norms,” Fuzzy Set and Systems, Vol. 124, No. 3, 2001, pp. 271-288. doi:10.1016/S0165-0114(01)00098-7

   P. Hájek, “Metamathematics of Fuzzy Logic,” Kluwer Academic Publishers, Dordrecht, 1998.

   G. J. Wang and H. J. Zhou, “Introduction to Mathematical Logic and Resolution Principle,” 2nd Edition, Science in China Press, Beijing, 2006 (in Chinese).

   G. J. Wang, “A Formal Deductive System for Fuzzy Propositional Calculus,” Chinese Science Bulletin, Vol. 42, No. 14, 1997, pp. 1521-1525.

   J. C. Zhang, “Some Properties of the Roots of Theories in Propositional Logic Systems,” Computers and Mathematics with Applications, Vol. 55, No. 9, 2008, pp. 2086- 2093. doi:10.1016/j.camwa.2007.08.035

   J. C. Zhang and X. Y. Yang, “Some Properties of Fuzzy Reasoning in Propositional Fuzzy Logic Systems,” Information Sciences, Vol. 180, No. 23, 2010, pp. 4661- 4671. doi:10.1016/j.ins.2010.07.035

   S. Gottwald, “A Treatise on Many-Valued Logics, Studies in Logic and Computation,” Research Studies Press, Baldock, 2001.

   G. J. Wang, “Theory of Non-Classical Mathematical Logic and Approximate Reasoning,” Science in China Press, Beijing, 2000.

   D. Dubois, J. Lang and H. Prade, “Fuzzy Set in Approximate Reasoning,” Fuzzy Sets and Systems, Vol. 40, No. 1, 1991, pp. 143-244. doi:10.1016/0165-0114(91)90050-Z

Top