Let 2 be a finite set of join dependencies (JDs), multivalued dependencies (MVDs) and functional dependencies (IDS). To test whether .% implies an MVD X -+ Y or an PD X -+ A, the procedure in [ 31 first generates the dependency basis DEP( X) of X with respect to 2. Then, X + Y if and only if Y is the union of some elements in DEP( X) , and X -+ A if and only if A E DEP( X), and there is an PD V...

We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the unrestricted implication problem for inclusion, functional, and embedded multivalued dependencies in the unirelational case.

There is a well-known algorithm for determining when a decomposition ˆ {R1,R2, . . . ,Rm} of a database relation scheme has a lossless join with respect to a set of functional dependencies. We ®rst present a reformulation of this algorithm in terms of set closures. For the special case of mˆ 2, there is a well-known explicit condition for losslessness. Our formulation extends this result for ge...

This paper introduces a new definition of fuzzy multivalued dependency, called α-fmvd, on the basis of the αequality of tuples as defined in [1]. Next the definition is shown to be consistent, i.e., it reduces to that of classical multivalued dependency (mvd) when the choice parameter takes the value one. Finally, a set of sound and complete inference axioms have been designed and proved for th...

The existence of approximate fixed points and approximate endpoints of the multivalued almost I-contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost I-contractions. The proved results unify and improve recent results of Amini-Harandi 2010 , M. Berinde and V. Berinde 2007 , Ćirić 2009 , M. Păc...

and Applied Analysis 3 In this paper, we generalize and modify the iteration of Abbas et al. 7 from two mapping to the infinite family mappings {Ti : i ∈ N} of multivalued quasi-nonexpansive mapping in a uniformly convex Banach space. Let {Ti} be a countable family of multivalued quasi-nonexpansive mapping from a bounded and closed convex subset K of a Banach space into P K with F : ⋂∞ i 1 F Ti...

We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize t...

This paper describes an efficient simulator for state transition analysis of multivalued continuous-time neural networks, where the multivalued transfer function of neuron is regarded as a stepwise constant one. Use of stepwise constant method enables to analyse the state transition of the network without solving explicitly the differential equations. This method also enables to select the opti...