Reasoning about concepts and similarity

2005

This work presents a dissimilarity measure for an expressive Description Logic endowed with the principal constructors employed in the standard representations for ontological knowledge. In particular, the focus is on the definition of a dissimilarity measure for the ALC description logic based both on the syntax and on the semantics of the descriptions. The measure is shown to be applicable to assess the dissimilarity for cases involving individuals.

2008

In this chapter we will introduce description logics, a family of logic-based knowledge representation languages that can be used to represent the terminological knowledge of an application domain in a structured way. We will first review their provenance and history, and show how the field has developed.

Fuzzy Sets and Systems, 2015

This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics. For this purpose we use concrete domains in the fuzzy description logic IALCE F (D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these objects.

2007

We extend the Description Logic ALC with a “typicality” operator T that allows us to reason about the prototypical properties and inheritance with exceptions. The resulting logic is called ALC + T. The typicality operator is intended to select the “most normal” or “most typical” instances of a concept. In our framework, knowledge bases may then contain, in addition to ordinary ABoxes and TBoxes, subsumption relations of the form “T(C) is subsumed by P”, expressing that typical C-members have the property P. The semantics of a typicality operator is defined by a set of postulates that are strongly related to Kraus-Lehmann-Magidor axioms of preferential logic P. We first show that T enjoys a simple semantics provided by ordinary structures equipped by a preference relation. This allows us to obtain a modal interpretation of the typicality operator. Using such a modal interpretation, we present a tableau calculus for deciding satisfiability of ALC + T knowledge bases. Our calculus give...

Lecture Notes in Computer Science, 2003

Description Logics (DLs) are a family of knowledge representation formalisms designed for the representation of terminological knowledge. A DL knowledge base consists (at least) of a set of concept definitions, namely of those concepts that are relevant for the specific application. Standard inference services provided by DL-based knowledge representation systems include tests whether each defined concept is satisfiable and the computation of the subsumption hierarchy of the defined concepts, i.e., of the specialisation relation between the defined concepts. Besides the well-defined semantics of DLs, these inference services make DLs suitable candidates for ontology languages, which have become of increasing importance due to the amount of information available electronically and the vision of the semantic web. For a variety of DLs, decision procedures, tight complexity bounds, and practical inference algorithms for the corresponding inference problems are known. It is clear that, to be of use as an ontology language, a description logic has to provide adequate expressive power, and we are thus concerned with the well-known trade-off between complexity and expressiveness. After a brief introduction to ontologies, we introduce the basic description logic ALC and describe how DLs can be used as ontology languages. Next, we sketch the relationship between DLs and other formalisms such as first order and modal logic and data base conceptual models. To give a broader view of DLs, some standard expressive means in DLs are mentioned as well as their modal logic counterparts and their effect on the complexity of the inference problems. In Section 3, we give an intuitive explanation of standard reasoning techniques employed for DLs and discuss their respective advantages: tableau-based algorithms turned out to be well-suited for implementations, whereas automata-based algorithms yield elegant upper complexity bounds for Exptime logics. In many cases, first a DL was proven to be in Exptime using automata before a tableau-based algorithm was designed and implemented.

Knowledge Engineering: Practice and …, 2008

Similarity measures play a key role in the Semantic Web perspective. Indeed, most of the ontology related operations such as ontology learning, ontology alignment, ontology ranking and ontology population are grounded on the notion of similarity. In the last few years several similarity functions have been proposed for measuring both concept similarity and ontology similarity. However, they lack of a comprehensive formal characterization that is able to explain their behavior and value added, in particular when the ontologies are formulated in description logics languages like OWL-DL. Concept similarity functions need to be able to deal with the high expressive power of the ontology representation language, and to convey the underlying semantics of the ontology to which concepts refer. We propose a semantic similarity measure for complex Description Logics concept descriptions that elicits the underlying ontology semantics. Furthermore, we theorize a set of criteria that a measure has to satisfy in order to be compliant with a semantic expected behavior.

1994

ion is a weil known mechanism in reasoning about individuals in concept-based systems. It consists in retrieving all the assertions relevant to a given individual a and collecting them into a single concept. Such concept has the property of being the most specific concept (expressible in the language) such that the individual a is an instance of. For this reason it is generally indicated by MSC(a) (Most Specific Concept). Abstraction, together with subsumption, allows one to perform instance checking. In fact, an algorithm for checking whether A 1= C(a) can work as follows: Step 1. compute MSC(a). Step 2. check whether C subsurnes MSC(a). This algorithm, called Abstraction/Subsumption, has been broadly exploited in actual systems (see [Quantz and Kindermann,1990; Nebel,1990]) . However, the problem of exploiting this algorithm is that, in general, it is not possible to completely fit in the information relevant to an individual into a single concept of the language. Let us clarify t...

1998

Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of concept description languages (description logics), originally to help filter out unimportant aspects of large concepts appearing in industrial-strength knowledge bases. This paper proposes a new approach to performing matching, based on a “concept-centered” normal form, rather than the more standard “structural subsumption” normal form for concepts.

Foundations of Artificial Intelligence, 2008

In this chapter we will introduce description logics, a family of logic-based knowledge representation languages that can be used to represent the terminological knowledge of an application domain in a structured way. We will first review their provenance and history, and show how the field has developed. We will then introduce the basic description logic ALC in some detail, including definitions of syntax, semantics and basic reasoning services, and describe important extensions such as inverse roles, number restrictions, and concrete domains. Next, we will discuss the relationship between description logics and other formalisms, in particular first order and modal logics; the most commonly used reasoning techniques, in particular tableau, resolution and automata based techniques; and the computational complexity of basic reasoning problems. After reviewing some of the most prominent applications of description logics, in particular ontology language applications, we will conclude with an overview of other aspects of description logic research, and with pointers to the relevant literature.

Journal of Intelligent Information Systems, 2015

Similarity assessment is a key operation in case-based reasoning and other areas of artificial intelligence. This paper focuses on measuring similarity in the context of Description Logics (DL), and specifically on similarity between individuals. The main contribution of this paper is a novel approach based on measuring similarity in the space of Conjunctive Queries, rather than in the space of concepts. The advantage of this approach is two fold. On the one hand it is independent of the underlying DL, and thus, there is no need to design similarity measures for different DL, and on the other hand, the approach is computationally more efficient than searching in the space of concepts.