An important line of research within the field of fuzzy DLs is the computation of an equivalent crisp representation of a fuzzy ontology. In this short paper, we discuss the relation between tractable fuzzy DLs and tractable crisp representations. This relation heavily depends on the family of fuzzy operators considered. Introduction. Despite the undisputed success of ontologies, classical onto...

in the present paper, a partial order on a non- archimedean fuzzymetric space under the  lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

We extend Makkai’s proof of strong amalgamation (push-outs of monos along arbitrary maps are monos) from the category of Heyting algebras to a class which includes the categories of symmetric bounded distributive lattices, symmetric Heyting algebras, Heyting modal S4-algebras, Heyting modal bi-S4-albegras, and Lukasiewicz n-valued algebras. We also extend and improve Pitt’s proof that strong am...

Fuzzy Logic was initiated in 1965 [1], [2], [3], by Lotfi A. Zadeh , professor for computer science at the University of California in Berkeley. Basically, Fuzzy Logic (FL) is a multivalued logic, that allows intermediate values to be defined between conventional evaluations like true/false, yes/no, high/low, etc. Notions like rather tall or very fast can be formulated mathematically and proces...

Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent?s rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer...

Two-layer modal syntax is based on two propositional languages (lower and upper one) and a modal language (a collection of modalities together with their arities) and features three kinds of formulae: (i) non-modal formulae build using lower propositional language, (ii) atomic modal formulae obtained by applying the modalities to non-modal ones, and (iii) complex modal formulae built from the a...

Very recently, a (fuzzy modal) logic to reason about coherent conditional probability, in the sense of de Finetti, has been introduced by the authors. Under this approach, a conditional probability ð j Þ is taken as a primitive notion defined over conditional events of the form ‘‘’ given ’’, ’j for short, where is not the impossible event. The logic, called FCP(L ), exploits an idea already use...

Autoepistemic logic is an important formalism for nonmonotonic reasoning originally intended to model an ideal rational agent reflecting upon his own beliefs. Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent?s rational beliefs on gradable propositions. It has recently been shown that, in the same way as autoepistemic logic generalizes answer...