Abstract
In various works, L.A. Zadeh has introduced fuzzy quantifiers, fuzzy usuality modifiers, and fuzzy likelihood modifiers. This paper provides these notions with a unified semantics and uses this to define a formal logic capable of expressing and validating arguments such as ‘Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly’. In effect, these are classical Aristotelean syllogisms that have been “qualified” through the use of fuzzy quantifiers. It is briefly outlined how these, together with some likelihood combination rules, can be used to address some well-known problems in the theory of nonmonotonic reasoning. The work is aimed at future applications in expert systems and robotics, including both hardware and software agents.
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References
J. Doyle, A truth maintenance system, Artificial Intelligence, 12 (1979) 231–272.
B. Smith and G. Kelleher, eds., Reason Maintenance Systems and their Applications, Ellis Horwood, Chichester, England, 1988.
A.N. Kolmogorov, Foundations of the Theory of Probability, 2nd English Edition, Chelsea, New York, 1956.
J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA, 1988.
D. Touretzky, Implicit ordering of defaults in inheritance systems, in: Proceedings of the Fifth National Conference on Artificial Intelligence, AAAI’84, Austin, TX (Morgan Kaufmann, Los Altos, CA (1984) 322– 325.
D. Touretzky, J.E. Horty, and R.H. Thomason, A clash of intuitions: the current state of nonmonotonic multiple inheritance systems, in Proceedings of IJCAI-87, Milan, Italy, 1987, pp. 476–482.
D.G. Schwartz, Dynamic reasoning with qualified syllogisms, Artificial Intelligence, 93 (1997) 103–167.
L.A. Zadeh, Fuzzy logic and approximate reasoning (in memory of Grigore Moisil), Synthese 30 (1975) 407–428.
L.A. Zadeh, PRUF—a meaning representation language for natural languages, International Journal of Man-Machine Studies 10 (1978) 395–460.
L.A. Zadeh, A computational approach to fuzzy quantifiers in natural languages, Computers and Mathematics 9 (1983) 149–184.
L.A. Zadeh, Fuzzy probabilities, Information Processing and Management 20 (1984) 363–372.
L.A. Zadeh, Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions, IEEE Transactions on Systems, Man, and Cybernetics 15 (1985) 754–763.
L.A. Zadeh, Outline of a theory of usuality based on fuzzy logic, in: A. Jones, A. Kaufmann, and H.-J. Zimmerman, eds., Fuzzy Sets Theory and Applications (Reidel, Dordrecht, 1986) 79–97.
Zadeh and R.E. Bellman, Local and fuzzy logics, in: J.M. Dunn and G. Epstein, eds., Modern Uses of Multiple-Valued Logic (Reidel, Dordrecht, 1977) 103–165.
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Schwartz, D.G. (2010). A Logic for Qualified Syllogisms. In: Elleithy, K. (eds) Advanced Techniques in Computing Sciences and Software Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3660-5_8
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DOI: https://doi.org/10.1007/978-90-481-3660-5_8
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