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...

Linear independent component analysis (ICA) learns simple cell receptive fields fromnatural images.Here,we show that linear complexvalued ICA learns complex cell properties from Fourier-transformed natural images, i.e. two Gabor-like filters with quadrature-phase relationship. Conventional methods for complex-valued ICA assume that the phases of the output signals have uniform distribution. We ...

A problem stated by Höhle in his book “Many-valued Topology and Applications” is solved. The problem consists of finding a necessary and sufficient condition for a stratified L-filter to be induced by a -filter in the sense of Lemma 4.4.3 in this book. The condition given is proved to be equivalent to the condition considered in Proposition 4.4.4 in this book in the case of complete MV -algebra...

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 generalize the notion of complete binary relation on complete lattice to residuated lattice valued ordered sets and show its properties. Then we focus on complete fuzzy tolerances on fuzzy complete lattices and prove they are in one-to-one correspondence with extensive isotone Galois connections. Finally, we prove that fuzzy complete lattice, factorized by a complete fuzzy tolerance, is agai...

The most often applied non-numerical uncertainty degrees are those taking their values in complete lattices, but also their weakened versions may be of interest. In what follows, we introduce and analyze possibilistic distributions and measures taking values in finite upper-valued possibilistic lattices, so that only for finite sets of such values their supremum is defined. For infinite sets of...

This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.

We develop a numerical framework for the quantum analogue of the “classical” lattice Boltzmann method (LBM), with the Maxwell-Boltzmann distribution replaced by the Fermi-Dirac function. To accommodate the spin density matrix, the distribution functions become 2× 2-matrix valued. We show that the efficient, commonly used BGK approximation of the collision operator is valid in the present settin...