A Qualitative Approach to Syllogistic Reasoning

In this paper we present a new approach to a symbolic treatment of quantified statements having the following form “QA's are B's”, knowing that A and B are labels denoting sets, and Q is a linguistic quantifier interpreted as a proportion evaluated in a qualitative way. Our model can be viewed as a symbolic generalization of statistical conditional probability notions as well as a symbolic generalization of the classical probabilistic operators. Our approach is founded on a symbolic finite M-valued logic in which the graduation scale of M symbolic quantifiers is translated in terms of truth degrees. Moreover, we propose symbolic inference rules allowing us to manage quantified statements.

[1]  Daniel Pacholczyk,et al.  Qualitative Reasoning with Quantified Assertions , 2000, AI&M.

[2]  Didier Dubois,et al.  A Symbolic Approach to Reasoning with Linguistic Quantifiers , 1992, UAI.

[3]  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.

[4]  Ronald P. Loui,et al.  Edited transcription of the workshop on defeasible reasoning with specificity and multiple inheritance St. Louis, April 1989 , 1990, SGAR.

[5]  Léa Sombé.  Reasoning under incomplete information in artificial intelligence: A comparison of formalisms using a single example , 1990, Int. J. Intell. Syst..

[6]  Ronald Prescott Loui.  Workshop on Defeasible Reasoning with Specificity and Multiple Inheritance , 1991, AI Mag..

[7]  Michael Reinfrank,et al.  Non-Monotonic Reasoning , 1989, Lecture Notes in Computer Science.

[8]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[9]  H. Jeffreys,et al.  The Theory of Probability , 1896 .

[10]  Manfred Jaeger,et al.  Default reasoning about probabilities , 1995 .

[11]  Henry E. Kyburg,,et al.  The Reference Class , 1983, Philosophy of Science.

[12]  Mohamed Yasser Khayata.  Contribution au traitement logico-symbolique des quantificateurs proportionnels vagues , 1999 .

[13]  Didier Dubois,et al.  On fuzzy syllogisms , 1988, Comput. Intell..

[14]  Daniel Pacholczyk,et al.  Contribution au traitement logico-symbolique de la connaissance , 1992 .

[15]  L. M. M.-T..  Theory of Probability , 1929, Nature.

[16]  T. Fine.  Theories of Probability: An Examination of Foundations , 1973 .

[17]  Daniel Pacholczyk,et al.  A qualitative theory of uncertainty , 1992, Fundam. Informaticae.

[18]  H. Kyburg,et al.  Nomic probability and the foundations of induction , 1990 .

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

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

[21]  Joseph Y. Halpern,et al.  From Statistical Knowledge Bases to Degrees of Belief , 1996, Artif. Intell..

[22]  K. J. Evans.  Representing and Reasoning with Probabilistic Knowledge , 1993 .

[23]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[24]  Peter C. Cheeseman,et al.  An inquiry into computer understanding , 1988, Comput. Intell..

[25]  Yang Xiang,et al.  Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra? , 1989, UAI.