CONSTRAINT SOLVING OVER MULTI-VALUED LOGICS — APPLICATION TO DIGITAL CIRCUITS by Francisco de Moura e Castro Ascensão de Azevedo Supervisor: Professor Pedro M. C. C. Barahona Departamento de Informática Due to usage conditions, hazardous environments or intentional causes, physical and virtual systems are subject to faults in their components, which may affect their overall behaviour. In a ‘bla...

This paper surveys some polarity-based knowledge representational and automated reasoning techniques in the domain of many-valued logics.

We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels, and that reasoning with these lo...

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. In the last decade, mathematical fuzzy logic has been developed as a discipline studying formal many-valued systems arising from fuzzy set theory. In this paper we study to what extent different systems of fuzzy logic are paraconsistent, identifying which f...

Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional log...

Many-Valued logics have been developed to represent mathematical model of imprecision, vagueness, uncertainty and ambiguity in the information. In real world each and every species is vague, human knowledge and the natural languages have a bunch of vagueness or imprecise information. This paper attempts to present three main theories of many-valued logics to treat the vagueness: Fuzzy Logic, Va...

The practical employment of automated deduction systems requires the user to input problem statements in a well-formed string representation. While this presentation is usually fixed by the respective system, the various language dialects of the TPTP library are meanwhile accepted as a de-facto standard for all current automated theorem provers based on classical logics. In the context of reaso...

Even though it is not very often admitted, partial functions do play a signiicant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional lo...

This paper is a survey of the connections between threevalued logics and rough sets from the point of view of incomplete information management. Based on the fact that many three-valued logics can be put under a unique algebraic umbrella, we show how to translate three-valued conjunctions and implications into operations on ill-known sets such as rough sets. We then show that while such transla...

This work introduces the concept language ALC F M which is an extension of ALC to many-valued logics. ALC F M allows to express vague concepts, e.g. more or less enlarged or very small. To realize this extension to many-valued logics, the classical notions of satissability and subsumption had to be modiied appropriately. For example, ALC F M-concepts are no longer either satissable or unsatissa...