In this paper, we investigate the many-valued version of coalgebraic modal logic through predicate lifting approach. Coalgebras, understood as generic transition systems, can serve semantic structures for various kinds logics. A well-known result in is that its completeness be determined at one-step level. We generalize to finitely case by using canonical model construction. prove logics based ...

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...

We propose a new definition of Representation theorem for many-valued modal logics, based on a complete latice of algebraic truth values, and define the stronger relationship between algebraic models of a given logic L and relational structures used to define the Kripke possible-world semantics for L. Such a new framework offers clear semantics for the satisfaction algebraic relation, based on ...

To further increase the speed of computation, this paper aims to design and implement digital circuits entirely within the domain of multi-valued logic. In a fourvalued logic circuit, each wire carries two bits at a time, each logic gate operates two bits at once, and each memory cell records two bits at one time. To make the multi-valued computation possible, this paper describes a simple four...

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...

Like in the case of classical logic and other non-standard logics, a variety of complexity-related questions can be asked in the context of many-valued logic. Some questions, such as the complexity of the sets of satisfiable and valid formulas in various logics, are completely standard; others, such as the maximal size of representations of many-valued connectives, only make sense in a many-val...