Fernando Bobillo

fuzzyDL: An expressive fuzzy description logic reasoner

In this paper we present fuzzyDL, an expressive fuzzy description logic reasoner.We present its salient features, including some novel concept constructs and queries, and examples of use cases: matchmaking and fuzzy control.

Fuzzy ontology representation using OWL 2

The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such information within current standard languages and tools. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies using OWL 2 annotation properties. We also report on some prototypical implementations: a plug-in to edit fuzzy ontologies using OWL 2 annotations and some parsers that translate fuzzy ontologies represented using our methodology into the languages supported by some reasoners.

Fuzzy description logics with general t-norms and datatypes

Fuzzy description logics (DLs) are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs still present several limitations. In this work we face two problems: the common restriction to Zadeh and Lukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets. In particular, we propose a semantics based on the use of a general left-continuous t-norm and an involutive negation (specially focused on Product logic) and, furthermore, we show how to handle functional concrete roles relating individuals of the domain and strings, real or integer numbers.

Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ

Fuzzy Description Logics are a formalism for the representation of structured knowledge affected by imprecision or vagueness. They have become popular as a language for fuzzy ontology representation. To date, most of the work in this direction has focused on the so-called Zadeh family of fuzzy operators (or fuzzy logic), which has several limitations. In this paper, we generalize existing proposals and show how to reason with a fuzzy extension of the logic SROIQ, the logic behind the language OWL 2, under finitely many-valued Lukasiewicz fuzzy logic. We show for the first time that it is decidable over a finite set of truth values by presenting a reasoning preserving procedure to obtain a non-fuzzy representation for the logic. This reduction makes it possible to reuse current representation languages as well as currently available reasoners for ontologies.

A Crisp Representation for Fuzzy

Fuzzy Description Logics are a family of logics which allow the representation of (and the reasoning with) structured knowledge affected by imprecision and vagueness. They were born to overcome the limitations of classical Description Logics when dealing with such kind of knowledge, but they bring out some new challenges, requiring an appropriate fuzzy language to be agreed and needing practical and highly optimized implementations of the reasoning algorithms. In the current paper we face these problems by presenting a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of the Description Logic

\cal SHOIN

\cal SHOIN

with Fuzzy Nominals and General Concept Inclusions

, which makes possible to reuse a crisp representation language as well as currently available reasoners, which have demonstrated a very good performance in practice. As additional contributions, we define the syntax and semantics of a novel fuzzy version of the nominal construct and allow to reason within fuzzy general concept inclusions.

CRISP REPRESENTATIONS AND REASONING FOR FUZZY ONTOLOGIES

Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. Fuzzy Description Logics were born to represent the former type of knowledge, but they require an appropriate fuzzy language to be agreed on and an important number of available resources to be adapted. This paper faces these problems by presenting a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of the logic

On the failure of the finite model property in some Fuzzy Description Logics

\mathcal{SROIQ}\mathbf{(D)}

An OWL Ontology for Fuzzy OWL 2

which includes fuzzy nominals and trapezoidal membership functions, and uses Godel implication in the semantics of fuzzy concept and role subsumption. This reduction makes it possible to reuse a crisp representation language as well as currently available reasoners. Our procedure is optimized with respect to related work, reducing the size of the resulting knowledge base. Finally, we also suggest some further optimizations before applying crisp reasoning.