In order to investigate a many valued logical system whose proportional value is given in a lattice, in 1993 Y. Xu [12] first established the lattice implication algebra by combining lattice and implication algebra, and explored many useful structures. The ideal theory serves a vital function for the development of lattice implication algebras. Y. Xu, Y.B. Jun and E.H. Roh [6] introduced the no...

We present a framework for fully automated compositional verification of μ-calculus specifications over multi-valued systems, based on multivalued abstraction and refinement. Multi-valued models are widely used in many applications of model checking. They enable a more precise modeling of systems by distinguishing several levels of uncertainty and inconsistency. Successful verification tools su...

In [8], Dontchev and Hager have shown that a monotone set-valued map defined from a Banach space to its dual which satisfies the Aubin property around a point (x, y) of its graph is actually single-valued in a neighbourhood of x. We prove a result which is the counterpart of the above for quasimonotone set-valued maps, based on the concept of single-directional property. As applications, we pro...

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations ⊖ and ⊕ of L are uniquely determined by their system of neighbourhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L.

A lattice ciphertext policy attribute based encryption (CP-ABE) scheme is presented, in which the ciphertext policy achieved is the AND-gates on multi-valued attributes. The previous construction with AND-gates on multi-valued attributes as ciphertext policy is based on bilinear paring technology. In this paper, inspired by the recent progress of lattice identity based encryption scheme, we ach...

We prove a Filippov type existence theorem for solutions of a fractional differential inclusion defined by a nonconvex set-valued map with Dirichlet boundary conditions. The method consists in application of the contraction principle in the space of selections of the set-valued map instead of the space of solutions.

Given a Hamiltonian torus action the image of the momentum map is a convex polytope; this famous convexity theorem of Atiyah, Guillemin and Sternberg still holds when the action is not required to be Hamiltonian. Our generalization of the convexity theorem states that, given a symplectic torus action, the momentum map can be defined on an appropriate covering of the manifold and has as image a ...

We examine results of gain-of-function experiments on retinocollicular maps in knock-in mice [Brown et al. (2000) Cell 102:77]. In wild-type mice the temporalnasal axis of retina is mapped to the rostral-caudal axis of superior colliculus (SC). The established map is single-valued, which implies that each point on retina maps to a single termination zone (TZ) in SC. In homozygous Isl2/EphA3 kno...