DeLorean: A Reasoner for Fuzzy OWL 1.1

In this paper we present a fuzzy version of SHOIN (D), the corresponding Description Logic of the ontology description language OWL DL. We show that the representation and reasoning capabilities of fuzzy SHOIN (D) go clearly beyond classical SHOIN (D). We present its syntax and semantics. Interesting features are that concrete domains are fuzzy and entailment and subsumption relationships may hold to some degree in the unit interval [0, 1].

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2012

Ontologies have succeeded as a knowledge representation formalism in many domains of application. Nevertheless, they are not suitable to represent vague or imprecise information. To overcome this limitation, several extensions to classical ontologies based on fuzzy logic have been proposed. Even though different fuzzy logics lead to fuzzy ontologies with very different logical properties, the combined use of different fuzzy logics has received little attention to date. This paper proposes a fuzzy extension of the Description Logic SROIQ -the logic behind the ontology language OWL 2that joins Gödel and Zadeh fuzzy logics. We analyze the properties of the new fuzzy Description Logic in order to provide guidelines to ontology developers to exploit the best features of each fuzzy logic. The proposal also considers degrees of truth belonging to a finite set of linguistic terms rather than numerical values, thus being closer to real experts' reasonings. We prove the decidability of the combined logic by presenting a reasoning preserving procedure to obtain a crisp representation for it. This result is generalized to offer a similar reduction that can be applied when any other finite t-norms, t-conorms, negations or implications are considered in the logic.

Journal of Artificial …, 2007

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N ). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN , as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN .

2007

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 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 SROIQ which uses Gödel implication in the semantics of fuzzy concept and role subsumption. This reduction allows to reuse a crisp representation language as well as currently available reasoners. Our procedure is optimized with respect to the related work, reducing the size of the resulting knowledge base, and is implemented in DeLorean, the first reasoner supporting fuzzy OWL DL.

… Reasoning for the …, 2008

The last couple of years it is widely acknowledged that uncertainty and fuzzy extensions to ontology languages, like Description Logics (DLs) and OWL, could play a significant role in the improvement of many Semantic Web (SW) applications. Many of the tasks of SW like trust, matching, merging, ranking usually involve confidence or truth degrees that one requires to represent and reason about. Fuzzy DLs are able to represent vague concepts such as a "Tall" person, a "Hot" place, a "MiddleAged" person, a "near" destination and many more. In the current paper we present a fuzzy extension to the DL SHIN . First, we present the semantics while latter a detailed reasoning algorithm that decides most of the key inference tasks of fuzzy-SHIN . Finally, we briefly present the fuzzy reasoning system FiRE, which implements the proposed algorithm and two use case scenarios where we have applied fuzzy DLs through FiRE.

Lecture Notes in Computer Science, 2008

The last couple of years it is widely acknowledged that uncertainty and fuzzy extensions to ontology languages, like Description Logics (DLs) and OWL, could play a significant role in the improvement of many Semantic Web (SW) applications. Many of the tasks of SW like trust, matching, merging, ranking usually involve confidence or truth degrees that one requires to represent and reason about. Fuzzy DLs are able to represent vague concepts such as a "Tall" person, a "Hot" place, a "MiddleAged" person, a "near" destination and many more. In the current paper we present a fuzzy extension to the DL SHIN . First, we present the semantics while latter a detailed reasoning algorithm that decides most of the key inference tasks of fuzzy-SHIN . Finally, we briefly present the fuzzy reasoning system FiRE, which implements the proposed algorithm and two use case scenarios where we have applied fuzzy DLs through FiRE.

1998

Description Logics (DLs, for short) allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with crisp, well defined concepts. That is, concepts for which the problem whether an individual is an instance of it is a yes/no question. More often than not, the concepts encountered in the real world do not have a precisely defined criteria of membership: we may say that an individual is an instance of a concept only to a certain degree, depending on the individual's properties. Concepts of this kind are rather vague than precise. As fuzzy logic directly deals with the notion of vagueness and imprecision, it offers an appealing foundation for a generalisation of DLs to vague concepts. In this paper we present a general fuzzy DL, which combines fuzzy logic with DLs. We define its syntax, semantics and present constraint propagation calculi for reasoning in it.

International Journal of Approximate Reasoning, 2009

Classical ontologies are not suitable to represent vague pieces of information, which has lead to the birth of Fuzzy Description Logics as an appropriate formalism to represent this type of knowledge. Different families of fuzzy operators lead to Fuzzy Description Logics with different properties. This paper studies Fuzzy Description Logics under a semantics given by the Gödel family of fuzzy operators. We investigate some logical properties and show the decidability of a fuzzy extension of the logic SROIQ, theoretical basis of the language OWL 1.1, by providing a reasoning preserving procedure to obtain a crisp representation for it. Additionally, we show how to represent some types of concept and role modifiers.

Information Sciences, 2011

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 Łukasiewicz 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. be very useful as ontology languages . For instance, OWL Lite, OWL DL and OWL 2 are close equivalents to SHIF ðDÞ; SHOIN ðDÞ and SROIQðDÞ, respectively .

Uncertainty and Intelligent information Systems, 2008

Description Logic Programs (DLPs), which combine the expressive power of classical description logics and logic programs, are emerging as an important ontology description language paradigm. In this work, we present fuzzy DLPs, which extend DLPs by allowing the representation of vague/imprecise information.