8,146 research outputs found
Gödel Description Logics
In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC
On similarity in fuzzy description logics
This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics . For this purpose we use concrete domains in the fuzzy description logic IALCEF(D)IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these object
On the similarity relation within fuzzy ontology components
Ontology reuse is an important research issue. Ontology
merging, integration, mapping, alignment and versioning
are some of its subprocesses. A considerable research work has
been conducted on them. One common issue to these subprocesses
is the problem of defining similarity relations among ontologies
components. Crisp ontologies become less suitable in all domains
in which the concepts to be represented have vague, uncertain
and imprecise definitions. Fuzzy ontologies are developed to
cope with these aspects. They are equally concerned with the
problem of ontology reuse. Defining similarity relations within
fuzzy context may be realized basing on the linguistic similarity
among ontologies components or may be deduced from their
intentional definitions. The latter approach needs to be dealt
with differently in crisp and fuzzy ontologies. This is the scope
of this paper.ou
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