| Klawonn, F. 1995. Prolog extensions to many-valued logics. In Hhle, U. and Klement, E.P. (eds), Non-Classical Logics and their Applications to Fuzzy Subsets, Kluwer Academic Publishers, pp. 271-289. |
....In fact, soft computing is not a single methodology, but a partnership of fuzzy logic, probabilistic reasoning and neuro computing ( 38] and in this paper we consider only the first two partners. Fuzzy logic and probabilistic logic have been applied to extend both logic programs (e.g. 15] [24], 29] 32] 28] and object oriented models (e.g. 7] 33] 36] 14] to deal with vagueness and uncertainty often encountered in practical problems. However, research on combining all together logic programming, object oriented programming and soft computing appears to be sporadic. The ....
....systems can be roughly classified into two groups with respect to whether they involve fuzzy sets in programs or not. Systems that do not involve fuzzy sets usually have formulas weighted by real numbers in the interval [0, 1] interpreted as truth or uncertainty degrees, e.g. 31] 15] and [24]. Systems that involve fuzzy sets, which we call fuzzy set logic programming, include those of [34] 4] 20] 37] and [8] Only fuzzy set logic programming systems can be used with the proposed framework to represent and reasoning with fuzzy set values in class and object properties. In ....
Klawonn, F. 1995. Prolog extensions to many-valued logics. In Hhle, U. and Klement, E.P. (eds), Non-Classical Logics and their Applications to Fuzzy Subsets, Kluwer Academic Publishers, pp. 271-289.
....it is obviously sufficient to restrict to implication clauses of the form (2) for soundness and completeness. How we can make use of these results for an implementation is shown in section 4. The same soundness and completeness results can be obtained for the infinite valued logic with T = 0; 1] [14] for the price that the value th (a) cannot be obtained by a finite number of direct derivations. In [14] also the Godel implication is considered as a possible truth function for the implication. A Prolog system based on this implication and the set of truth values T = 0; 1] can be shown ....
....How we can make use of these results for an implementation is shown in section 4. The same soundness and completeness results can be obtained for the infinite valued logic with T = 0; 1] 14] for the price that the value th (a) cannot be obtained by a finite number of direct derivations. In [14] also the Godel implication is considered as a possible truth function for the implication. A Prolog system based on this implication and the set of truth values T = 0; 1] can be shown to be equivalent to Prolog based on possibilistic logic [16] For such [0; 1] valued logical system a ....
F. Klawonn, Prolog Extensions to Many--Valued Logics. In: U. Hohle, E.P. Klement (eds.), Proc. 14th Linz Seminar on Fuzzy Set Theory: Non--Classical Logics and their Applications. Johannes Kepler Universit at, Linz (1992), 42--45.
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