We investigate an extension of Description Logics (DL) with higher-order capabilities, based on Henkin-style semantics. Our study starts from the observation that the various possibilities of adding higher-order con- structs to a DL form a spectrum of increasing expres- sive power, including domain metamodeling, i.e., using concepts and roles as predicate arguments. We argue that higher-order features of this type are sufficiently rich and powerful for the modeling requirements aris- ing in many relevant situations, and therefore we carry out an investigation of the computational complexity of satisfiability and conjunctive query answering in DLs extended with such higher-order features. In particular, we show that adding domain metamodeling capabilities to SHIQ (the core of OWL 2) has no impact on the complexity of the various reasoning tasks. This is also true for DL-LiteR (the core of OWL 2 QL) under suit- able restrictions on the queries.

The research on low-complexity nonmonotonic description logics recently identified a fragment of EL with bottom, supporting defeasible inheritance with overriding, where reasoning can be carried out in polynomial time. We contribute to that framework by supporting more axiom schemata and all the concept constructors of EL++ without increasing asymptotic complexity. Moreover, we show that all the syntactic restrictions we adopt are necessary by proving several coNP-hardness results.

OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language. Consistency and entailment checking are known to be undecidable for OWL 2 Full. We have translated a large fragment of the OWL 2 Full semantics into first-order logic, and used automated theorem proving systems to do reasoning based on this theory. The results are promising, and indicate that this approach can be applied in practice for effective OWL reasoning, beyond the capabilities of current Semantic Web reasoners. This is an extended version of a paper with the same title that has been published at CADE 2011, LNAI 6803, pp. 446-460. The extended version provides appendices with additional resources that were used in the reported evaluation.

Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. We complete here the analysis by showing that knowledge base satisfiability is also an undecidable problem for Lukasiewicz Logic.

Debugging of ontologies is an important prerequisite for their wide-spread application, especially in areas that rely upon everyday users to create and maintain knowledge bases, as in the case of the Semantic Web. Recent approaches use diagnosis methods to identify causes of inconsistent or incoherent ontologies. However, in most debugging scenarios these methods return many alternative diagnoses, thus placing the burden of fault localization on the user. This paper demonstrates how the target diagnosis can be identified by performing a sequence of observations, that is, by querying an oracle about entailments of the target ontology. We exploit a-priori probabilities of typical user errors to formulate information-theoretic concepts for query selection. Our evaluation showed that the proposed method significantly reduces the number of required queries compared to myopic strategies. We experimented with different probability distributions of user errors and different qualities of the a-priori probabilities. Our measurements showed the advantageousness of information-theoretic approach to query selection even in cases where only a rough estimate of the priors is available.

The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics (DLs): if a general L-TBox implicitly defines an L-concept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in DLs. In this paper a complete classification of Beth definability is provided for extensions of the basic DL ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableau-based algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in first-order logic then we show how to compute them in EXPTIME.

We review recent results on inferencing for SROEL(×), a description logic that subsumes the main features of the W3C recommendation OWL EL. Rule-based deduction systems are developed for various reasoning tasks and logical sublanguages. Certain feature combinations lead to increased space upper bounds for materialisation, suggesting that efficient implementations are easier to obtain for suitable fragments of OWL EL.

The problem of grasping is widely studied in the The problem of semantic part decomposition is still an robotics community. This project focuses on the open problem and, to the best of our knowledge, there are identification of object graspable features using images no tools available to automatically create a fuzzy ontology and object structural information. The primary from raw data taken from an image. The use of fuzzy DLs for aim is the creation of a framework in which the information object recognition has been investigated in some works such gathered by the vision system can be integrated as [Hudelot et al., 2008], in which little advantage is taken with automatically generated knowledge, from the (partial) fuzzy extension and from the expressivity modelled by means of fuzzy description logics. of the used logic (i.e., no cardinality restrictions are used); furthermore, a preliminary phase of semantic annotation of the images by domain experts has to be performed.

Log-linear description logics are a family of probabilistic logics integrating various concepts and methods from the areas of knowledge representation and reasoning and statistical relational AI. We define the syntax and semantics of log-linear description logics, describe a convenient representation as sets of first-order formulas, and discuss computational and algorithmic aspects of probabilistic queries in the language. The paper concludes with an experimental evaluation of an implementation of a log-linear DL reasoner.

For my thesis work I am developing a method for evaluating and standardizing ontologies based on an integration of the Basic Formal Ontology (BFO) and OntoClean. BFO serves as the upper ontology for the domain ontologies of the Open Biomedical Ontologies (OBO) Foundry. The OBO Foundry initiative is a collaborative effort for developing interoperable, science-based ontologies. OntoClean is an approach for the quality assurance of ontologies, and helps a modeler detect when the subsumption relation is used improperly. Ontologies developed for OBO use include some that have been ratified, and others holding the status of “candidate”. To maintain consistency between ontologies, it is important to establish formal principled criteria that a candidate ontology must meet for ratification. The formalisms that result from our integration will serve as criteria an OBO Foundry candidate ontology must satisfy in order to be ratified. The formalisms will also serve as a constraints within a prototype of an ontology editor that interactively asks a modeler questions that helps alleviate constraint violations.