Reasoning about Explanations for Negative Query Answers in DL-Lite

In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for instance and conjunctive query answering over DL-Lite ontologies by adopting abductive reasoning; that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning tasks we consider existence and recognition of an explanation, and relevance and necessity of a given assertion for an explanation. We characterize the computational complexity of these problems for arbitrary, subset minimal, and cardinality minimal explanations

Conjunctive Query Answering in Rough EL

Rough Description Logics have recently been studied as a means for representing and reasoning with imprecise knowledge. Real-world applications need to exploit reasoning over such knowledge in an efficient way. We describe how the combined approach to query answering can be extended to the rough setting. In particular, we extend both the canonical model and the rewriting procedure such that rough queries over rough EL ontologies can be answered by considering this information alone

Reasoning in Many Dimensions : Uncertainty and Products of Modal Logics

Probabilistic Description Logics (ProbDLs) are an extension of Description Logics that are designed to capture uncertainty. We study problems related to these logics. First, we investigate the monodic fragment of Probabilistic first-order logic, show that it has many nice properties, and are able to explain the complexity results obtained for ProbDLs. Second, in order to identify well-behaved, in best-case tractable ProbDLs, we study the complexity landscape for different fragments of ProbEL; amongst others, we are able to identify a tractable fragment. We then study the reasoning problem of ontological query answering, but apply it to probabilistic data. Therefore, we define the framework of ontology-based access to probabilistic data and study the computational complexity therein. In the final part of the thesis, we study the complexity of the satisfiability problem in the two-dimensional modal logic KxK. We are able to close a gap that has been open for more than ten years

Ontology-Based Data Access and Integration

An ontology-based data integration (OBDI) system is an information management system consisting of three components: an ontology, a set of data sources, and the mapping between the two. The ontology is a conceptual, formal description of the domain of interest to a given organization (or a community of users), expressed in terms of relevant concepts, attributes of concepts, relationships between concepts, and logical assertions characterizing the domain knowledge. The data sources are the repositories accessible by the organization where data concerning the domain are stored. In the general case, such repositories are numerous, heterogeneous, each one managed and maintained independently from the others. The mapping is a precise specification of the correspondence between the data contained in the data sources and the elements of the ontology. The main purpose of an OBDI system is to allow information consumers to query the data using the elements in the ontology as predicates. In the special case where the organization manages a single data source, the term ontology-based data access (ODBA) system is used

A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases

Ontologies and rules are usually loosely coupled in knowledge representation formalisms. In fact, ontologies use open-world reasoning while the leading semantics for rules use non-monotonic, closed-world reasoning. One exception is the tightly-coupled framework of Minimal Knowledge and Negation as Failure (MKNF), which allows statements about individuals to be jointly derived via entailment from an ontology and inferences from rules. Nonetheless, the practical usefulness of MKNF has not always been clear, although recent work has formalized a general resolution-based method for querying MKNF when rules are taken to have the well-founded semantics, and the ontology is modeled by a general oracle. That work leaves open what algorithms should be used to relate the entailments of the ontology and the inferences of rules. In this paper we provide such algorithms, and describe the implementation of a query-driven system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic) rules under the well-founded semantics and a (monotonic) ontology, represented by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic Programming (TPLP

Combined FO rewritability for conjunctive query answering in DL-Lite

Standard description logic (DL) reasoning services such as satisfiability and subsumption mainly aim to support TBox design. When the design stage is over and the TBox is used in an actual application, it is usually combined with instance data stored in an ABox, and therefore query answering becomes the most importan

Ontology-based data access with databases: a short course

Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop