We propose Clopen Knowledge Bases (CKBs) as a new formalism combining Answer Set Programming (ASP) with ontology languages based on first-order logic. CKBs generalize the prominent r-hybrid and DL+LOG languages of Rosati, and are more flexible for specification of problems that combine open-world and closed-world reasoning. We argue that the guarded negation fragment of first-order logic(GNFO)—a very expressive fragment that subsumes many prominent ontology languages like Description Logics (DLs) and the guarded fragment—is an ontology language that can be used in CKBs while enjoying decidability for basic reasoning problems. We further show how CKBs can be used with expressive DLs of the ALC family, and obtain worst-case optimal complexity results in this setting. For DL-based CKBs, we define a fragment called separable CKBs (which still strictly subsumes r-hybrid and DL+LOG knowledge bases), and show that they can be rather efficiently translated into standard ASP programs. This approach allows us to perform basic inference from separable CKBs by reusing existing efficient ASP solvers. We have implemented the approach for separable CKBs containing ontologies in the DL ALCH, and present in this paper some promising empirical results for real-life data. They show that our approach provides a dramatic improvement over a naive implementation based on a translation of such CKBs into dl-programs.
Answering ontology mediated queries (OMQs) has received much attention in the last decade, but the big gap between practicable algorithms for lightweight ontologies, that are supported by implemented reasoners, and purely theoretical algorithms for expressive ontologies that are not amenable to implementation, has only increased. Towards narrowing the gap, we propose an algorithm to compile a representation of sets of models for ALCHI ontologies, which is sufficient for answering any monotone OMQ. Rather than reasoning for specific ABoxes, or being fully data-independent, we use generic descriptions of families of ABoxes, given by what we call profiles. Our model compilation algorithm runs on TBoxes and sets of profiles, and supports the incremental addition of new profiles. To illustrate the potential of our approach for OMQ answering, we implement a rewriting into an extension of Datalog for OMQs comprising reachability queries, and provide some promising evaluation results.
Ontology-based data access (OBDA) has emerged as a paradigm for accessing heterogeneous and incomplete data sources. A fundamental reasoning service in OBDA, the ontology mediated query (OMQ) answering has received much attention from the research community. However, there exists a disparity in research carried for OMQ algorithms for lightweight DLs which have found their way into practical implementations, and algorithms for expressive DLs for which the work has had mainly theoretical oriented goals. In the dissertation, a technique that leverages the structural properties of data to help alleviate the problems that typically arise when answering the queries in expressive settings is developed. In this paper, a brief summary of the technique along with the different algorithms developed for OMQ for expressive DLs is given.
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