Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoidM andQ-enriched categories are introduced for quantales L andQ, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, la...

A tight binding approach based on the Bogoliubov-de Gennes approach has been used to calculate the DC Josephson current for a lattice model for S-GNR-S junctions , for short junctions with respect to superconducting coherence length. We calculate the phase, length, width and chemical potential dependence at the Josephson junction and discuss the similarities and differences with regard to the t...

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

Based on the general form of -resolution principle for a lattice-valued logic with truth-values defined in a latticevalued logical algebra structure lattice implication algebra, the further extended -resolution method in this lattice-valued logic is discussed in the present paper in order to increase the efficiency of the resolution method. Firstly, -quasi-lock semantic resolution method in lat...

As a continuation of our research work on resolutionbased automated reasoning approaches for latticevalued logic systems with truth-values in a latticevalued logical algebraic structure – lattice implication algebra (LIA), in the present paper, we prove thatα resolution for lattice-valued first-order logic ( ) LF X based on LIA can be equivalently transformed into that for lattice-valued propos...