Fuzzy logic programming

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Fuzzy Logic Programming

Fuzzy logic programming is an interesting chapter of formal fuzzy logic in which the attention is focused on fuzzy theories named fuzzy programs. A fuzzy program is a fuzzy set of program clauses in a first order language. As in the case of classical logic programming we can define the notion of least fuzzy Herbrand model of a fuzzy program and we can calculate such a model by a fixed point technique (see P. Vojtas 1966, P. Vojtas 2001 and D. Dubois D. and H. Prade 1996). In accordance with fuzzy logic ideas, the aim is to manage information vague in nature.

Strictly connected with the notion of fuzzy logic programming is the one of logic programming based on bilattices (see M. Fitting 1991). Another connection between fuzzy logic and logic programming is suggested similarity logic defined in (see M.S.Ying 1994). This is a first order logic in which the inference rules run taking in account of a synonimy relation between predicate names. In turn such a relation is formalized by a fuzzy equivalence. In the particular case of logic programming the unification process is relaxed since the identity is substituted by a graded equivalence (see Formato, Gerla , Sessa 2000). Finally, observe that it is possible to consider fuzzy logic programming as a logical basis for fuzzy control (see Gerla 2005).

Bibliography

  • Baldwin J.F., Martin T.P., Pilsworth B.W., Fril: Fuzzy and Evidential Reasoning in Arti-cial Intelligence, Wiley, New York, 1995.
  • Biacino L., Gerla G., Ying M. S.: Approximate reasoning based on similarity, Math. Log. Quart., 46 (2000), 77-86.
  • Dubois D., Prade H., What are fuzzy rules and how to use them, Fuzzy Sets and Systems, 84 (1996) pp. 169-185.
  • Gerla G., Fuzzy Logic Programming and fuzzy control, Studia Logica, 79 (2005) 231-254.
  • Fitting M., Bilattices and semantics of logic programming, Journal of Logic Programming, 11 (1991) pp. 91-116.
  • Formato F., Gerla G., Sessa M., Similarity-based unification, Fundamenta Informaticae, 41 (2000), 393-414.
  • Lee R.C.T., Fuzzy logic and the resolution principle, J. Assoc. Comput. Mach. 19 (1) (1972) 119–129.
  • Vojtas P., Fuzzy logic programming, Fuzzy Sets and Systems, 124 (2001) pp. 361-370.
  • Vojtas P., Many valued logic programming handling uncertainty in AI, Proceedings of LACS, Warsawa, 1966.
  • Ying M. S., A logic for approximate reasoning, J. Symbolic Logic, 59 (1994).
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