Flattening is a method to make a de nite clause function-free. For a de nite clause C, attening replaces every occurrence of a term f(t 1 ; ; t n ) in C with a new variable v and adds an atom p f (t 1 ; ; t n ; v) with the associated predicate symbol p f with f to the body of C. Here, we denote the resulting function-free de nite clause from C by at(C). In this paper, we discuss the relationshi...

In this paper we present some Boolean algebras in the form of lattice by using the fuzzy implication. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature. KeywordsFuzzy logic connectives, Fuzzy implication, Algebras, Lattice.

We introduce an implication-with-possible-exceptions and define validity of rules-withpossible-exceptions by means of the topological notion of a full subset. Our implication-with-possibleexceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other ...

The present paper discusses a generalization operator based on the-subsumption ordering between Horn clauses introduced by the author elsewhere. It has been shown that-subsumption is strictly stronger than-subsumption and a local equivalent of generalized subsumption. With some language restrictions it is decidable and possesses some other useful properties. Most importantly it allows deening a...

For the last decade, fuzzy controllers have been applied with great success to a variety of domains. Nevertheless the underlying theoretical framework still remains unsatisfactory. One of the key questions still open is concerned with approximate reasoning. How should we determine the eeect of applying the fuzzy rule IF x is ~ A THEN y is ~ B] to ~ A 0 with ~ A 0 , ~ A, and ~ B being fuzzy sets...