On fuzzy syllogisms

This paper provides a systematic treatment of possibly imprecisely or vaguely specified numerical quantifiers in default syllogisms, following an approach initiated by Zadeh. The obtained propagation rules are derived from simple properties of relative cardinality or, equivalently, conditional probability. Uncertainty in the description of numerical quantifiers is handled using possibility theory and, particularly, fuzzy arithmetic. The advantages of this default reasoning method are its ability to model any kind of quantifier and to build new defaults by chaining existing ones, in a rigorous manner. This approach also emphasizes the difference between two types of uncertain pieces of knowledge, i.e., conjectures versus general rules.

[1]  Lotfi A. Zadeh,et al.  Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Arie Tzvieli.  Possibility theory: An approach to computerized processing of uncertainty , 1990, J. Am. Soc. Inf. Sci..

[3]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[4]  Lotfi A. Zadeh,et al.  PRUF—a meaning representation language for natural languages , 1978 .

[5]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[6]  E. W. Adams,et al.  The logic of conditionals , 1975 .

[7]  Lotfi A. Zadeh,et al.  A theory of commonsense knowledge , 1983 .

[8]  Henri Prade.  Some Issues in Approximate and Plausible Reasoning in the Framework of a Possibility Theory-Based Approach , 1987 .

[9]  G Paass,et al.  Consistent evaluation of uncertain reasoning systems , 1987 .

[10]  James P. Delgrande,et al.  A First-Order Conditional Logic for Prototypical Properties , 1987, Artif. Intell..

[11]  L. Zadeh.  The role of fuzzy logic in the management of uncertainty in expert systems , 1983 .

[12]  Robert Stalnaker.  A Theory of Conditionals , 2019, Knowledge and Conditionals.

[13]  Amnon Rapoport,et al.  Direct and indirect scaling of membership functions of probability phrases , 1987 .

[14]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[15]  Didier Dubois,et al.  On the combination of uncertain or imprecise pieces of information in rule-based systems-A discussion in the framework of possibility theory , 1988, Int. J. Approx. Reason..

[16]  S. V. Chesnokov,et al.  The effect of semantic freedom in the logic of natural language , 1987 .

[17]  J. Ross Quinlan,et al.  Inferno: A Cautious Approach To Uncertain Inference , 1986, Comput. J..

[18]  Elaine Rich,et al.  Default Reasoning as Likelihood Reasoning , 1983, AAAI.

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

[20]  Benjamin Cohen,et al.  Models of Concepts , 1984, Cogn. Sci..

[21]  Didier Dubois,et al.  A review of fuzzy set aggregation connectives , 1985, Inf. Sci..

[22]  Judea Pearl,et al.  Fusion, Propagation, and Structuring in Belief Networks , 1986, Artif. Intell..

[23]  Edward E. Smith,et al.  Gradedness and conceptual combination , 1982, Cognition.

[24]  Matthew L. Ginsberg,et al.  Non-Monotonic Reasoning Using Dempster's Rule , 1984, AAAI.