Fuzzy logic programming: Difference between revisions
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=== Fuzzy Logic Programming === | === 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 thecnique (see the papers of P. Vojtas). In accordance with fuzzy logic ideas, the aim is to manage information vague in nature. | 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 thecnique (see the papers of P. Vojtas and D. Dubois D. and H. Prade). 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 [Fitting]. | Strictly connected with the notion of fuzzy logic programming is the one of logic programming based on bilattices [Fitting]. Another connection between fuzzy logic and logic programming is suggested ''similarity logic'' defined in [Ying]. This is a first order logic in which the inference rules run taking in accout 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 F., Gerla G., Sessa M.]). | ||
Finally, observe that it is possible to consider fuzzy logic programming as a logical basis for fuzzy control (see [Gerla G.]). | |||
Another connection between fuzzy logic and logic programming is suggested ''similarity logic'' defined in [Ying]. This is a first order logic in which the inference rules run taking in accout 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. | |||
== Bibliography == | == Bibliography == | ||
Revision as of 04:59, 30 November 2007
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 thecnique (see the papers of P. Vojtas and D. Dubois D. and H. Prade). 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 [Fitting]. Another connection between fuzzy logic and logic programming is suggested similarity logic defined in [Ying]. This is a first order logic in which the inference rules run taking in accout 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 F., Gerla G., Sessa M.]). Finally, observe that it is possible to consider fuzzy logic programming as a logical basis for fuzzy control (see [Gerla G.]).
Bibliography
- 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.
- 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).