In this paper, we address the complexity issue of reasoning with implication constraints. We consider the IC-RFT problem, which is the problem of deciding whether a conjunctive yes/no query always produces the empty relation (\no" answer) on database instances satisfying a given set of implication constraints, as a central problem in this respect. We show that several other important problems, ...

A fuzzy implication, commonly defined as a two-place operation on the unit interval, is an extension of the classical binary implication. It plays important roles in both mathematical and applied sides of fuzzy set theory. Besides the basic axioms, there are many potential fuzzy implication axioms, among which eight are widely used in the literature. Different fuzzy implications satisfying diff...

Designing a DL system poses the problem of the trade-off between power of expression and complexity. In spite of their rich expressive capacity, the or and not constructors are usually avoided because of the intractability of the resulting subsomption algorithm. So is implication. However, implication may constitute an interesting compromise between expressive power and tractability. We present...

this study aims at review and discuss types of places mentioned in al-hareeri`s maqamaat and their significance and relevance to mankind`s religious, socioeconomic and literary life within the necessary righteous and healthy needed environment. this study endeavors to disclose the broad lines of hareeri`s theory and its semantic aspects of place and the mutual influence of mankind and place on ...

It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting im...

A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper...

A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which coincides with the relative pseudocomplementation if P is relatively psudocomplemented. We characterise this operation and study some elementary properties of upper...

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. A given set of FDs does not interact with a given set of INDs if logical implication of any FD can be determined solely by the given set of FDs, and logical implication of any IND can be determined solely by the given set of INDs. The set...

The law of contraposition with respect to a negation (usually strong) is one of the most studied properties in the theory of fuzzy implication functions. We already know some methods for modifying an implication with the aim that the new implication satisfies this property, these methods are called contrapositivisation. In this paper we present two new methods of contrapositivisation with respe...

This paper studies the implication relations between the AGM postulates ( 7) and (+̇7) under non-classical logics, namely intuitionistic logic, paraconsistent logic, G3 and G3'. In order to do so, some theorems on the implication relations between such postulates are drawn for logics with a special set of axioms. These are later used to deduce similar results under the four logics of interest. T...