Foundation of credibilistic logic

In this paper, credibilistic logic is introduced as a new branch of uncertain logic system by explaining the truth value of fuzzy formula as credibility value. First, credibilistic truth value is introduced on the basis of fuzzy proposition and fuzzy formula, and the consistency between credibilistic logic and classical logic is proved on the basis of some important properties about truth values. Furthermore, a credibilistic modus ponens and a credibilistic modus tollens are presented. Finally, a comparison between credibilistic logic and possibilistic logic is given.

[1]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[2]  Richard C. T. Lee.  Fuzzy Logic and the Resolution Principle , 1971, JACM.

[3]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[4]  Donald Michie,et al.  Machine Intelligence 7 , 1975 .

[5]  H. J. Skala.  On many-valued logics, fuzzy sets, fuzzy logics and their applications , 1978 .

[6]  Henri Prade,et al.  A Computational Approach to Approximate and Plausible Reasoning with Applications to Expert Systems , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Ronald R. Yager,et al.  Inference in a Multivalued Logic System , 1985, Int. J. Man Mach. Stud..

[8]  Nils J. Nilsson,et al.  Probabilistic Logic * , 2022 .

[9]  James J. Buckley,et al.  A fuzzy expert system , 1986 .

[10]  Didier Dubois,et al.  Necessity Measures and the Resolution Principle , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Piero P. Bonissone,et al.  Summarizing and propagating uncertain information with triangular norms , 1990, Int. J. Approx. Reason..

[12]  Didier Dubois,et al.  Possibilistic Logic, Preferential Models, Non-monotonicity and Related Issues , 1991, IJCAI.

[13]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 2: logical approaches , 1991 .

[14]  L. Bolc,et al.  Many-Valued Logics , 1992 .

[15]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[16]  J. A. Goguen,et al.  The logic of inexact concepts , 1969, Synthese.

[17]  Xiang Li,et al.  A Sufficient and Necessary Condition for Credibility Measures , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[18]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[19]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[20]  Xiang Li,et al.  Maximum Entropy Principle for Fuzzy Variables , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[21]  Jinwu Gao,et al.  The Independence of Fuzzy Variables with Applications to Fuzzy Random Optimization , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[22]  Baoding Liu,et al.  Entropy of Credibility Distributions for Fuzzy Variables , 2008, IEEE Transactions on Fuzzy Systems.