Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying \x is true" and satisfying the \dequotation schema" ' Tr(') for all sentences '? This problem is investigated in the frame of Lukasiewicz innnitely valued logic.

The purpose of this paper is to make some practically relevant results in automated theorem proving available to many-valued logics with suitable modifications. We are working with a notion of many-valued first-order clauses which any finitely-valued logic formula can be translated into and that has been used several times in the literature, but in an ad hoc way. We give a many-valued version o...

In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three­ valued logic (true, false, and "don't care"). The three-valued approach allows the construction of "compressed" constraint systems which have the same solut...

A general approach to automated theorem proving for all rst-order nite-valued logics that can be deened truth-functionally is described. The suggested proof procedure proceeds in two, largely independent, steps. First, logic-speciic translation calculi are used to generate clause forms for arbitrary formulas of a many-valued logic. The worst-case complexity of the translation rules is analysed ...

Due to the high density and the low consumption power in the digital integrated circuits, mostly technology of CMOS is used. During the past times, the Metal oxide silicon field effect transistors (MOSFET) had been used for the design and implementation of the digital integrated circuits because they are compact and also they have the less consumption power and delay to the other transistors. B...

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued Łukasiewicz logic Ł3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by Ł3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in whic...

Usually, fuzzy logic (and multi-valued logics in general) are viewed as drastically different from the usual 2valued logic. In this paper, we show that while on the surface, there indeed seems to be a major difference, a more detailed analysis shows that even in the theories based on the 2-valued logic, there naturally appear constructions which are, in effect, multi-valued, constructions which...

The paper considers the fundamental notions of manyvalued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite v...

Suppose (Ω, ∗, I) is a commutative, unital quantale. Categories enriched over Ω can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain adjunctions, they can be reformulated in the many-valued setting in terms of categorical postulations. So, it is possible, by aid o...