Abstract
Fuzzy description logics, the formalism behind fuzzy ontologies, are an important mathematical method with applications in many artificial intelligence scenarios. This paper proposes the first specific algorithms to solve two reasoning tasks with respect to a fuzzy ontology: the instance retrieval and the realization problem. Our algorithms are based on a reduction of the number of optimization problems to solve by merging some of them. Our experimental evaluation shows that the novel algorithm to solve the instance retrieval outperforms the previous algorithm, and that in practice it is common to be able to solve a single optimization problem.
Highlights
Description Logics (DLs for short) [1] are a popular family of logics to represent structured knowledge, in ontologies
We propose two specific algorithms to solve the instance retrieval and the realization problem with respect to a fuzzy ontology
There are several fuzzy versions of each crisp ontology, we considered here fuzzy ontologies of the form l.66, with a semantics given by Łukasiewicz fuzzy logic and 66% fuzzy axioms
Summary
Description Logics (DLs for short) [1] are a popular family of logics to represent structured knowledge, in ontologies. Mathematics 2020, 8, 154 it requires retrieving pairs hC, αi such that i belongs to C with degree greater or equal than α > 0 Because this can be computed using a best entailment degree test for each concept C in the fuzzy ontology, no specific algorithms have been designed. We propose two specific algorithms to solve the instance retrieval and the realization problem with respect to a fuzzy ontology Such algorithms are based on an extension of an optimization technique called optimization partitioning, originally proposed in [19] and extended in [20].
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