Ontology-Mediated Querying with Horn Description Logics

An ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that occur when working with OMQs and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice

Parikh Automata on Infinite Words

Parikh automata on finite words were first introduced by Klaedtke and Rue{\ss} [Automata, Languages and Programming, 2003]. In this paper, we introduce several variants of Parikh automata on infinite words and study their expressiveness. We show that one of our new models is equivalent to synchronous blind counter machines introduced by Fernau and Stiebe [Fundamenta Informaticae, 2008]. All our models admit {\epsilon}-elimination, which to the best of our knowledge is an open question for blind counter automata. We then study the classical decision problems of the new automata models

Remarks on Parikh-recognizable omega-languages

Several variants of Parikh automata on infinite words were recently introduced by Guha et al. [FSTTCS, 2022]. We show that one of these variants coincides with blind counter machine as introduced by Fernau and Stiebe [Fundamenta Informaticae, 2008]. Fernau and Stiebe showed that every $\omega$-language recognized by a blind counter machine is of the form $\bigcup_iU_iV_i^\omega$ for Parikh recognizable languages $U_i, V_i$, but blind counter machines fall short of characterizing this class of $\omega$-languages. They posed as an open problem to find a suitable automata-based characterization. We introduce several additional variants of Parikh automata on infinite words that yield automata characterizations of classes of $\omega$-language of the form $\bigcup_iU_iV_i^\omega$ for all combinations of languages $U_i, V_i$ being regular or Parikh-recognizable. When both $U_i$ and $V_i$ are regular, this coincides with B\"uchi's classical theorem. We study the effect of $\varepsilon$-transitions in all variants of Parikh automata and show that almost all of them admit $\varepsilon$-elimination. Finally we study the classical decision problems with applications to model checking.Comment: arXiv admin note: text overlap with arXiv:2302.04087, arXiv:2301.0896

Reverse engineering queries in ontology-enriched systems: the case of expressive horn description logic ontologies

We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples? We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE

How to Approximate Ontology-Mediated Queries

We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as the class of databases whose treewidth is bounded by a constant. We determine the computational complexity and the relative completeness of the resulting approximations. (Almost) all of them reduce the data complexity from coNP-complete to PTime, in some cases even to fixed-parameter tractable and to linear time. While approximations of kind (1) also reduce the combined complexity, this tends to not be the case for approximations of kind (2). In some cases, the combined complexity even increases

Ontology-Mediated Querying mit Horn-Beschreibungslogiken

An ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that occur when working with OMQs and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice

Granular Spatial Calculi of Relative Directions or Movements with Parallelism: Consistent Account (Short Paper)

The OPRA* calculus family, originally suggested by Frank Dylla, adds parallelism to the OPRA calculus family which is very popular in Qualitative Spatio-temporal Reasoning (QSTR). Adding parallelism enables the direct representation of parallel moving objects, which is relevant in many applications like traffic monitoring. However, it turned out that it is hard to derive a sound geometric analysis. So far no sound spatial reasoning was supported. Our new generic analysis based on combining condensed semantics lower bounds with upper bounds from algebraic mappings of related calculi already leads to a close and sound approximization. This approximization can be easily augmented with a manual analysis of few geometrically underconstrained cases and then yields a complete analysis of possible configurations in this oriented point framework. This for the first time enables sound standard QSTR constraint reasoning for the OPRA* calculus family