In order to process the linguistic-valued information with uncertainty in the financial decisionmaking, the present work uses a lattice-valued logical algebra lattice implication algebra to deal with both comparable and incomparable linguistic truth-values. A new personal financial decision auxiliary modeling framework based on the lattice-ordered linguistic truth-valued logic is proposed. The ...

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...

In multi-valued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as a lattice element. In this paper we present new algorithms for multi-valued model checking. We first show how to reduce multi-valued model checking with any distributive DeMorgan lattice to standard, two-valued model checking. We then present a direct, automata-theoretic a...

Unlike monotone single-valued functions, multi-valued mappings may have none, one or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixed-points of multi-valued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these res...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

Multi-valued logics support the explicit modeling of uncertainty and disagreement by allowing additional truth values in the logic. Such logics can be used for verification of dynamic properties of systems where complete, agreed upon models of the system are not available. In this paper, we present an implementation of a symbolic model checker for multi-valued temporal logics. The model checker...

Orthomodular logic represented by a complete orthomodular lattice has been studied as a pertinent generalization of the two-valued logic, Boolean-valued logic, and quantum logic. In this paper, we introduce orthomodular logic valued models for set theory generalizing quantum logic valued models introduced by Takeuti as well as Boolean-valued models introduced by Scott and Solovay, and prove a g...

In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new binary sequent calculi (each sequent is a pair of formulae) for many valued logic with a finite set of truth values, and of Kripke-like semantics for it that is both sound and complete. We did not use the logic entailment based o...

This paper shows the best operators for sumof-products expressions. We first describe conditions of functions for product and sum operations. We examine all two-variable functions and select those that meet the conditions and then evaluate the number of product terms needed in the minimum sum-of-products expressions when each combination of selected product and sum functions is used. As a resul...