The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.

According to Frege’s principle the denotation of a sentence coincides with its truthvalue. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A ded...

The efficient evaluation of recursive views is a crucial issue in the research field of deductive databases. Results in this area are especially relevant for systems which will implement the new SQL:1999 standard, and hence will allow the definition of stratifiable recursive views. In particular, transformation-based solutions to query evaluation seem to be well-suited for extending existing re...

Update propagation in deductive databases can be implemented by combining rule rewriting and fixpoint computation, analogous to the way how query answering is performed via Magic Sets. For efficiency reasons, bottom-up propagation rules have to be subject to Magic rewriting, thus possibly loosing stratifiability. We propose to use the soft stratification approach for computing the well-founded ...

in this paper rst we dene the notions of positive implicativehyper mv -ideals of types 1,2,3 and 4 in hyper mv -algebras and we investigatethe relationship between of them . then by some examples we show that thesenotions are not equivalent. finally we give some relations between these notionsand the notions of (weak) hyper mv -ideals and (weak) hyper mv -deductivesystems of hyper mv -algebras.

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [2] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment ...

Lukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Lukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Lukasiewicz algebra by using a “truthpreserving” scheme. This deductive system...