1. Formulation of the problem 1:1: It is necessary to represent implication in expert systems Our knowledge of complex systems is often incomplete, and therefore, we have to rely on the expert's statements, These statements are usually formulated not in mathematical terms, but in words of natural languages. Fuzzy logic is a methodology for formalizing such statements. Since a large part of expe...

Inclusion dependencies are one of the most important database constraints. In isolation their finite and unrestricted implication problems coincide, are finitely axiomatizable, PSPACE-complete, and fixed-parameter tractable in their arity. In contrast, finite and unrestricted implication problems for the combined class of functional and inclusion dependencies deviate from one another and are ea...

| Logical inference starts with concluding that if B implies A, and B is true, then A is true as well. To describe probabilistic inference rules, we must therefore deene the probability of an implication \A if B". There exist two diierent approaches to deening this probability, and these approaches lead to diierent probabilistic inference rules: We may interpret the probability of an implicatio...

Relevant logics provide an alternative to classical implication that is capable of accounting for the relationship between the antecedent and the consequence of a valid implication. Relevant implication is usually explained in terms of information required to assess a proposition. By doing so, relevant implication introduces a number of cognitively relevant aspects in the definition of logical ...

The paper deals with fuzzy versions of the classical bi-implication, that is, extensions of classical bi-implication to the canonical domain of mathematical fuzzy logics, the real-valued unit interval [0, 1]. Our approach to fuzzy bi-implication may be summarized as follows: first, we recall a well-known approach to bi-implications, by Fodor and Roubens, via the direct axiomatization of the pro...

We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.

In the present paper we construct a new intuitionistic fuzzy implication, giving form to Goguen’s implication. Some of its basic properties are studied and illustrated with examples. Geometrical interpretations different forms implication given. Other discussed.

We study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of SQL’s NOT NULL constraints. Two different notions of implication are addressed: one where a dependency is implied by the given set of dependencies plus the underlying schema, and one where a dependency is implied by the given set of dependencies alone. We establish axiomat...

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...