A Set-Based Reasoner for the Description Logic DL4, xD

2015

In this paper we use results from Computable Set Theory as a means to represent and reason about description logics and rule languages for the semantic web. Specifically, we introduce the description logic DL〈 4LQS^R〉()--admitting features such as min/max cardinality constructs on the left-hand/right-hand side of inclusion axioms, role chain axioms, and datatypes--which turns out to be quite expressive if compared with SROIQ(), the description logic underpinning the Web Ontology Language OWL. Then we show that the consistency problem for DL〈 4LQS^R〉()-knowledge bases is decidable by reducing it, through a suitable translation process, to the satisfiability problem of the stratified fragment 4LQS^R of set theory, involving variables of four sorts and a restricted form of quantification. We prove also that, under suitable not very restrictive constraints, the consistency problem for DL〈 4LQS^R〉()-knowledge bases is NP-complete. Finally, we provide a 4LQS^R-translation of rules belongi...

ArXiv, 2017

We present an ongoing implementation of a \ke\space based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic $\dlssx$ (shortly $\shdlssx$). The reasoner checks the consistency of $\shdlssx$-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports $\shdlssx$-KBs serialized in the OWL/XML format. To the best of our knowledge, this is the first attempt to implement a reasoner for the consistency checking of a description logic represented via a fragment of set theory that can also classify standard OWL ontologies.

2016

Description logics (DLs) are a family of logic-based knowledge representation formalisms, which provide underlying semantics for modern ontology languages such as OWL 2. Reasoners for DLs are mostly specialised algorithms, which can answer questions such as whether an ontology as a whole is consistent, whether a certain concept in an ontology can be non-empty, or whether one concept subsumes another concept. Language extensions such as support for concrete domains (e.g. numbers) have been proposed in the past, but every extension typically requires the development of new reasoning algorithms. Some extensions have in fact never been implemented. This paper explores the use of CP technology for handling DL reasoning tasks. We show that CP modelling languages make it easy to extend DLs with new features, using a direct, high-level encoding into MiniZinc. Furthermore, our experiments show that modern CP solvers based on Lazy Clause Generation can be used as efficient DL reasoners. We pr...

Journal of automated …, 2007

We propose a new family of Description Logics (DLs), called DL-Lite, specifically tailored to capture basic ontology languages, while keeping low complexity of reasoning. Reasoning here means not only computing subsumption between concepts, and checking satisfiability of the whole knowledge base, but also answering complex queries (in particular, unions of conjunctive queries) over the instance level (ABox) of the DL knowledge base. We show that, for the DLs of the DL-Lite family, the usual DL reasoning tasks are polynomial in the size of the TBox, and query answering is LogSpace in the size of the ABox (i.e., in data complexity). To the best of our knowledge, this is the first result of polynomial time data complexity for query answering over DL knowledge bases. Notably our logics allow for a separation between TBox and ABox reasoning during query evaluation: the part of the process requiring TBox reasoning is independent of the ABox, and the part of the process requiring access to the ABox can be carried out by an SQL engine, thus taking advantage of the query optimization strategies provided by current Data Base Management Systems. Since it can be shown that even slight extensions to the logics of the DL-Lite family make query answering at least NLogSpace in data complexity, thus ruling out the possibility of using on-the-shelf relational technology for query processing, we can conclude that the logics of the DL-Lite family are the maximal DLs supporting efficient query answering over large amounts of instances.

On the Move to Meaningful …, 2008

Proceedings of the …, 2005

We propose a new Description Logic, called DL-Lite, specifically tailored to capture basic ontology languages, while keeping low complexity of reasoning. Reasoning here means not only computing subsumption between concepts, and checking satisfiability of the whole knowledge base, but also answering complex queries (in particular, conjunctive queries) over the set of instances maintained in secondary storage. We show that in DL-Lite the usual DL reasoning tasks are polynomial in the size of the TBox, and query answering is polynomial in the size of the ABox (i.e., in data complexity). To the best of our knowledge, this is the first result of polynomial data complexity for query answering over DL knowledge bases. A notable feature of our logic is to allow for a separation between TBox and ABox reasoning during query evaluation: the part of the process requiring TBox reasoning is independent of the ABox, and the part of the process requiring access to the ABox can be carried out by an SQL engine, thus taking advantage of the query optimization strategies provided by current DBMSs.

2002

Abstract In this paper our goal is to bridge two popular and wellstudied knowledge representation formalisms: description logics (DLs), and declarative logic programs (DLPs). In recent years there has been tremendous development in both fields in terms of theoretical studies and implementations.

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.

IFIP International Federation for Information Processing, 2006

The paper presents the architecture and design of a description logics (DLs) reasoner based on the Model Driven Architecture (MDA) methodology. The architecture relies on OMG's description logics metamodel, tableau metamodel, and model transformations using a language for model transformation. We show an example of DLs knowledge base using UML notation in context of MDA. The idea can be easily applied to implementation of a first-order logic theorem prover. The paper does not discuss implementation details of reasoning algorithms and the reasoner performance.

2013

Description Logics (DLs) are gaining a widespread adoption as the popularity of the Semantic Web increases. Traditionally, reasoning algorithms for DLs have been implemented in procedural languages such as Java or C++. In this paper, we present the system TRILL for “Tableau Reasoner for descrIption Logics in proLog”. TRILL answers queries to SHOIN (D) knowledge bases using a tableau algorithm. Prolog nondeterminism is used for easily handling non-deterministic expansion rules that produce more than one tableau. Moreover, given a query, TRILL is able to return instantiated explanations for the query, i.e., instantiated minimal sets of axioms that allow the entailment of the query. The Thea2 library is exploited by TRILL for parsing ontologies and for the internal Prolog representation of DL axioms.