Description Logics with Fuzzy Concrete Domains

International journal of …, 2010

Mathematical Fuzzy Logic Propositional and predicate t-norm based fuzzy logics Truth constants a b s t r a c t Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for dealing with vague concepts, commonly present in real applications.

Capturing Intelligence, 2006

This chapter introduces reasoning procedures for ALCQ + F (D), a fuzzy description logic with extended qualified quantification [D. Sánchez, A.G.B. Tettamanzi, Generalizing quantification in fuzzy description logics, in: Proceedings 8th Dortmund Fuzzy Days, Dortmund, Germany, 2004]. The language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on N and Q ∩ [0, 1] respectively. In order to reason about instances, the semantics of quantified expressions is defined by using method GD [M. Delgado, D. Sánchez, M. Vila, Fuzzy cardinality based evaluation of quantified sentences, Int. J. Approximate Reasoning 23 , 23-66], which is based on recently developed measures of the cardinality of fuzzy sets. The main contribution of this chapter is a procedure to calculate the fuzzy satisfiability of a fuzzy concept, which is a very important reasoning task. The procedure considers several different cases and provides direct solutions for the most frequent types of fuzzy concepts. In order to distinguish between these cases, a novel idea of concept independence is also introduced.

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.

2009

Fuzzy Description Logics are a family of logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs are open to be extend with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs with fuzzy truth values, allowing to state sentences such as "Tina is young is almost true".

2006

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). Interesting features are: (i) concept constructors are based on t-norm, t-conorm, negation and implication; (ii) concrete domains are fuzzy sets; (iii) fuzzy modifiers are allowed; and (iv) entailment and subsumption relationships may hold to some degree in the unit interval [0, 1]. mgb:Roadster (∃maker.{mg}) (∃speed.≤ 170km/h ) enzo:Car (∃maker.{ferrari}) (∃speed.> 350km/h ) tt:Car (∃maker.{audi}) (∃speed.= 243km/h ) Consider the knowledge base K = T , R, A . It is then easily verified that, e.g. K |= Roadster Car K |= mg:Maker K |= enzo:SportsCar K |= tt:¬SportsCar .

Proceedings of the 11th …, 2006

Description Logics (DLs) have been studied and applied successfully in quite a lot of fields (see eg [1]). To deal with vague and imprecise information in real-world applications, fuzzy ALC [7] introduces fuzzy concepts. As a more general case of fuzzy ALC, a DL framework ...

Journal of Artificial Intelligence Research, 2001

Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e. set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval.

2009 Ninth International Conference on Intelligent Systems Design and Applications, 2009

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, little attention has been given to the role of datatypes in fuzzy DLs. This paper presents a fuzzy DL with three kinds of extended datatype restrictions, together with the necessary rules to reason with them.

In this paper we introduce reasoning procedures for ALCQ + F , a fuzzy description logic with extended qualified quantification. The language allows for the definition of fuzzy quantifiers of the absolute and relative kind by means of piecewise linear functions on N and Q ∩ [0, 1] respectively. In order to reason about instances, the semantics of quantified expressions is defined based on recently developed measures of the cardinality of fuzzy sets. A procedure is described to calculate the fuzzy satisfiability of a fuzzy assertion, which is a very important reasoning task. The procedure considers several different cases and provides direct solutions for the most frequent types of fuzzy assertions.

2009

Abstract. In the current paper we study the reasoning problem for fuzzy SI (f-SI) under arbitrary continuous fuzzy operators. Our work can be seen as an extension of previous works that studied reasoning algorithms for f-SI, but focused on specific fuzzy operators, eg fKD-SI and of reasoning algorithms for less expressive fuzzy DLs, like fL-ALC and fP-ALC (fuzzy ALC under the Lukasiewicz and product fuzzy operators, respectively).