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Learning in Description Logics with Fuzzy Concrete Domains

Lisi F. A., Straccia U.

Fundamenta Informaticae

2015

Vol. 140, nr 3/4

373--391

Description Logics (DLs) are a family of logic-based Knowledge Representation (KR) formalisms, which are particularly suitable for representing incomplete yet precise structured knowledge. Several fuzzy extensions of DLs have been proposed in the KR field in order to handle imprecise knowledge which is particularly pervading in those domains where entities could be better described in natural language. Among the many approaches to fuzzification in DLs, a simple yet interesting one involves the use of fuzzy concrete domains. In this paper, we present a method for learning within the KR framework of fuzzy DLs. The method induces fuzzy DL inclusion axioms from any crisp DL knowledge base. Notably, the induced axioms may contain fuzzy concepts automatically generated from numerical concrete domains during the learning process. We discuss the results obtained on a popular learning problem in comparison with state-of-the-art DL learning algorithms, and on a test bed in order to evaluate the classification performance.

Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web

Lukasiewicz T.

Fundamenta Informaticae

2008

Vol. 82, nr 3

289-310

There are numerous semantic web applications where dealing with vagueness and imprecision plays an important role. Some examples of such applications are (i) multimedia information processing and retrieval, (ii) natural language interfaces to the Web, and (iii) ontology mapping and information retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to normal fuzzy description logic programs under the answer set semantics, which are a generalization of normal description logic programs (dl-programs) under the answer set semantics by fuzzy vagueness and imprecision in both the description logic and the logic program component. We define a canonical semantics of positive and stratified fuzzy dl-programs in terms of a unique least model and iterative least models, respectively. We then define the answer set semantics of general fuzzy dl-programs, and show in particular that all answer sets of a fuzzy dl-program are minimal models, and that the answer set semantics of positive and stratified fuzzy dl-programs coincides with their canonical least model and iterative least model semantics, respectively. We also provide a characterization of the canonical semantics of positive and stratified fuzzy dl-programs in terms of a fixpoint and an iterative fixpoint semantics, respectively. Furthermore, we provide a reduction of fuzzy dl-programs under the answer set semantics to normal dl-programs under the answer set semantics. Finally, we also describe a special case of fuzzy dl-programs where query processing can be done in polynomial time in the data complexity.