Víctor Gutiérrez-Basulto

Towards a unifying approach to representing and querying temporal data in description logics

Establishing a generic approach to representing and querying temporal data in the context of Description Logics (DLs) is an important, and still open challenge. The difficulty lies in that a proposed approach should reconcile a number of valuable contributions coming from diverse, yet relevant research lines, such as temporal databases and query answering in DLs, but also temporal DLs and Semantic Web practices involving rich temporal vocabularies. Within such a variety of influences, it is critical to carefully balance theoretical foundations with good prospects for reusing existing techniques, tools and methodologies. In this paper, we attempt to make first steps towards this goal. After providing a comprehensive overview of the background research and identifying the core requirements, we propose a general mechanism of defining temporal query languages for time-stamped data in DLs, based on combinations of linear temporal logics with first-order queries. Further, we advocate a controlled use of epistemic semantics in order to warrant practical query answering. We systematically motivate our proposal and highlight its basic theoretical and practical implications. Finally, we outline open problems and key directions for future research.

Complexity of branching temporal description logics

We study branching-time temporal description logics (TDLs) based on the DLs ALC and ℇL and the temporal logics CTL and CTL*. The main contributions are algorithms for satisfiability that are more direct than existing approaches, and (mostly) tight elementary complexity bounds that range from PTIME to 2EXPTIME and 3EXPTIME. A careful use of tree automata techniques allows us to obtain transparent and uniform algorithms, avoiding to deal directly with the intricacies of CTL*.

Conjunctive queries with negation over DL-Lite: a closer look

While conjunctive query (CQ) answering over DL-Lite has been studied extensively, there have been few attempts to analyse CQs with negated atoms. This paper deepens the study of the problem. Answering CQs with safe negation and CQs with a single inequality over DL-Lite with role inclusions is shown to be undecidable, even for a fixed TBox and query.Without role inclusions, answering CQs with one inequality is P-hard and with two inequalities coNP-hard in data complexity.

Description logics of context

Copyright: 2013 Oxford University Press. This is an ABSTRACT ONLY. The definitive version is published in Journal of Logic and Computation, pp 1-47

An update on query answering with restricted forms of negation

One of the most prominent applications of description logic ontologies is their use for accessing data. In this setting, ontologies provide an abstract conceptual layer of the data schema, and queries over the ontology are then used to access the data. In this paper we focus on extensions of conjunctive queries (CQs) and unions of conjunctive queries (UCQs) with restricted forms of negations such as inequality and safe negation. In particular, we consider ontologies based on members of the DL-Lite family. We show that by extending UCQs with any form of negated atoms, the problem of query answering becomes undecidable even when considering ontologies expressed in the core fragment of DL-Lite. On the other hand, we show that answering CQs with inequalities is decidable for ontologies expressed in DL-

{\mathcal{ALC}_\mathcal{ALC}}: A Context Description Logic

Lite^{\mathcal{H}}_{core}

Reverse Engineering Queries in Ontology-Enriched Systems: The Case of Expressive Horn Description Logic Ontologies

. To this end, we provide an algorithm matching the known coNP lower bound on data complexity. Furthermore, we identify a setting in which conjunctive query answering with inequalities is tractable. We regain tractability by means of syntactic restrictions on the queries, but keeping the expressiveness of the ontology.

Combining DL-Lite_{bool}^N with Branching Time: A gentle Marriage

We develop a novel description logic (DL) for representing and reasoning with contextual knowledge. Our approach descends from McCarthys tradition of treating contexts as formal objects over which one can quantify and express first-order properties. As a foundation we consider several common product-like combinations of DLs with multimodal logics and adopt the prominent (Kn)ALC. We then extend it with a second sort of vocabulary for describing contexts, i.e., objects of the second dimension. In this way, we obtain a two-sorted, two-dimensional combination of a pair of DLs ALC, called ALCALC. As our main technical result, we show that the satisfiability problem in this logic, as well as in its proper fragment (Kn)ALC with global TBoxes and local roles, is 2EX- PTIME-complete. Hence, the surprising conclusion is that the significant increase in the expressiveness of ALCALC due to adding the vocabulary comes for no substantial price in terms of its worst-case complexity.

A closer look at the probabilistic description logic prob- EL

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.

ALC ALC : a context description logic

We study combinations of the description logic DL-Lite_{bool}^N with the branching temporal logics CTL* and CTL. We analyse two types of combinations, both with rigid roles: (i) temporal operators are applied to concepts and to ABox assertions, and (ii) temporal operators are applied to concepts and Boolean combinations of concept inclusions and ABox assertions. For the resulting logics, we present algorithms for the satisfiability problem and (mostly tight) complexity bounds ranging from ExpTime to 3ExpTime.