We propose assertion-consistency (AC) semi-lattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multiple-viewpoint and multiple-valued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multipl...

In this paper, a double-layer modificatory linguistic truth-value lattice-valued evaluation method is presented. Its logic basic is based on modificatory linguistic truth-value lattice-valued proposition logic system MLTVLP(X) and operator modificatory linguistic truth-value lattice-valued proposition logic OMLTVLP(X). MLTVLP(X) and OMLTVLP(X) are similar to LTVLP(X) and MLTVLP(X), which have b...

A formalism is proposed for representing uncertain information on set-valued variables using the formalism of belief functions. A set-valued variableX on a domain Ω is a variable taking zero, one or several values in Ω. While defining mass functions on the frame 22 Ω is usually not feasible because of the double-exponential complexity involved, we propose an approach based on a definition of a ...

In this paper, we investigate the properties of antitone Galois connection and formal concepts. Moreover, we show that order reverse generating maps induce formal, attribute oriented and object oriented concepts on a complete residuated lattice.

Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results indicate two zones in parameter space where the dynamics shows the most complex patterns. These zones are located on the two edges of an absorbent region where t...

In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that...

We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete wavelet transform with real wavelets. Moreover, the hexagonal lattice allows to build wavelets having a more isotropic magnitude than on the C...

We consider the Miura map between the lattice KP hierarchy and the lattice modified KP hierarchy and prove that the map is canonical not only between the first Hamiltonian structures, but also between the second Hamiltonian structures.

Multiple-valued logics can be effectively used to reason about incomplete and/or inconsistent systems, e.g. during early software requirements or as the systems evolve. We specify multiple-valued logics using finite lattices. In this paper, we use lattice representation theory to cast the multiple-valued modelchecking problem in terms of symbolic operations on classical sets of states, provided...

We consider the lattice-reduction-aided detection scheme for 2×2 channels recently proposed by Yao and Wornell [11]. Using an equivalent real-valued substitute MIMO channel model their lattice reduction algorithm can be replaced by the well-known LLL algorithm, which enables the application to MIMO systems with arbitrary numbers of dimensions. We show how lattice reduction can also be favourabl...