Reasoning in ${\mathcal{ALC}}$ with Fuzzy Concrete Domains

Abstract

In the context of Description Logics (DLs) concrete domains allow to model concepts and facts by the use of concrete values and predicates between them. For reasoning in the DL ALC with general TBoxes concrete domains may cause undecidability. Under certain restrictions of the concrete domains decidability can be regained. Typically, the concrete domain predicates are crisp, which is a limitation for some applications. In this paper we investigate crisp ALC in combination with fuzzy concrete domains for general TBoxes, devise conditions for decidability, and give a tableau-based reasoning algorithm.

Decidability and Complexity of Fuzzy Description Logics

“…For instance, the picture of decidability and complexity for the case of general models is not as clear as the one described for witnessed models in Table 1, although some results have been obtained [15]. Extensions of FDLs with concrete domains [46,55] and other non-logical constructors need also to be studied in more detail. Nevertheless, our results provide an important map of the complexity landscape of fuzzy description logics, which can aid researchers and modeling experts alike in choosing a fuzzy description logic suitable for their needs.…”

Semantic Technologies for Situation Awareness

“…For almost a decade, the restrictions formulated in [51] were the only ones known to preserve decidability. In [57] we extend these conditions to fuzzy concrete domains. An important result of our project is that we were able to establish new restrictions that guarantee decidability [27], which are orthogonal to the previously known ones, and yield decidability for some interesting concrete domains over the integers that were not covered by the restrictions in [51].…”

Fuzzy Description Logics – A Survey

“…the total order on the natural numbers. In [80], the classical description logic ALC is extended with the use of fuzzy concrete domains, which provide built-in fuzzy predicates. In the context of FDLs, fuzzy concrete domains have also been studied in [18,98], but are usually restricted to unary concrete predicates.…”