There is a long tradition of the interest of logicians in computer science and of computer scientists in logic. On the one hand, many problems raised and investigated by logicians before the emergence of computer science turned out to be relevant for the new science. We may quote here the notion of algorithm, model theory or relational systems. On the other hand, some problems stemming from com...

We propose a combination of logic programming under the answer set semantics with the description logics SHIF(D) and SHOIN (D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set of description logic rules (or dl-rules) P . Such r...

As it is well-known, Lukasiewicz developed in [2] the many-valued propositional calculi based on two primitive connectives, negation N and implication C, which were defined semantically. Complete axiomatizations followed later on. Among the works on this argument, we mention Wajsberg [9], Rosser and Turquette [8], Mc Naughton [3], Rose and Rosser [7], Meredith [4], Chang [1], Rose [5], [6]. It ...

There has been a long tradition of the interest of logicians in computer science and of computer scientists in logic. On the one hand, many problems raised and investigated by logicians before the emergence of computer science turned out to be relevant for the new science. We may quote here the notion of algorithm , model theory or relational systems. On the other hand, some problems stemming f...

We present an approach where probabilistic logic is combined with default reasoning from conditional knowledge bases in Kraus et al.’s System P , Pearl’s System Z, and Lehmann’s lexicographic entailment. The resulting probabilistic generalizations of default reasoning from conditional knowledge bases allow for handling in a uniform framework strict logical knowledge, default logical knowledge, ...

This paper examines the motivation and foundations of fuzzy sets theory, now some 20 years old, particularly possible misconceptions about possible operators and relations to probability theory. It presents a standard uncertainty logic (SUI.) that subsumes standard propositional, fuzzy and probability logics, and shows how many key results may be derived within SUL without further constraints. ...

Chang’s MV-algebras are, on the one hand, the algebras of the infinite-valued Lukasiewicz calculus and, on the other hand, they are categorically equivalent to abelian lattice-ordered groups with a distinguished strong unit, for short, unital `-groups. The latter are a modern mathematization of the time-honored euclidean magnitudes with an archimedean unit. While for magnitudes the unit is no l...

In this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-Lukasiewicz operator. In fact Lukasiewicz t-norm is one of the four basic t-norms. A new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on ...

Formal approaches that aim at representing human reasoning should be evaluated based on how humans actually reason. One way in doing so, is to investigate whether psychological findings of human reasoning patterns are represented in the theoretical model. The computational logic approach discussed here is the so called weak completion semantics which is based on the three-valued Lukasiewicz log...