On Implementing Temporal Query Answering in DL-Lite

Ontology-based data access augments classical query answering over fact bases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We implemented temporal query answering w.r.t. ontologies formulated in the Description Logic DL-Lite. Focusing on temporal conjunctive queries (TCQs), which combine conjunctive queries via the operators of propositional linear temporal logic, we regard three approaches for answering them: an iterative algorithm that considers all data available; a window-based algorithm; and a rewriting approach, which translates the TCQs to be answered into SQL queries. Since the relevant ontological knowledge is already encoded into the latter queries, they can be answered by a standard database system. Our evaluation especially shows that implementations of both the iterative and the window-based algorithm answer TCQs within a few milliseconds, and that the former achieves a constant performance, even if data is growing over time

Temporal Query Answering in DL-Lite with Negation

Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DL-Lite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment

Temporal Query Answering in DL-Lite over Inconsistent Data

In ontology-based systems that process data stemming from different sources and that is received over time, as in context-aware systems, reasoning needs to cope with the temporal dimension and should be resilient against inconsistencies in the data. Motivated by such settings, this paper addresses the problem of handling inconsistent data in a temporal version of ontology-based query answering. We consider a recently proposed temporal query language that combines conjunctive queries with operators of propositional linear temporal logic and extend to this setting three inconsistency-tolerant semantics that have been introduced for querying inconsistent description logic knowledge bases. We investigate their complexity for DL-LiteR temporal knowledge bases, and furthermore complete the picture for the consistent case

Ontology-Mediated Query Answering for Probabilistic Temporal Data with EL Ontologies: Extended Version

Especially in the field of stream reasoning, there is an increased interest in reasoning about temporal data in order to detect situations of interest or complex events. Ontologies have been proved a useful way to infer missing information from incomplete data, or simply to allow for a higher order vocabulary to be used in the event descriptions. Motivated by this, ontology-based temporal query answering has been proposed as a means for the recognition of situations and complex events. But often, the data to be processed do not only contain temporal information, but also probabilistic information, for example because of uncertain sensor measurements. While there has been a plethora of research on ontologybased temporal query answering, only little is known so far about querying temporal probabilistic data using ontologies. This work addresses this problem by introducing a temporal query language that extends a well-investigated temporal query language with probability operators, and investigating the complexity of answering queries using this query language together with ontologies formulated in the description logic EL

Temporal Conjunctive Queries in Expressive DLs with Non-simple Roles

In Ontology-Based Data Access (OBDA), user queries are evaluated over a set of facts under the open world assumption, while taking into account background knowledge given in the form of a Description Logic (DL) ontology. Motivated by situation awareness applications, temporal conjunctive queries (TCQs) have recently been proposed as a useful extension of traditional OBDA to support the processing of temporal information. This paper extends the existing complexity analysis of TCQ entailment to very expressive DLs underlying the OWL 2 standard, and in contrast to previous work also allows for queries containing transitive roles.This is an extended version of the paper “Temporal Conjunctive Queries in Expressive Description Logics with Transitive Roles”, published in the Proceedings of the 28th Australasian Joint Conference on Artificial Intelligence (AI’15)

Ontology-mediated query answering over temporal data: a survey

We discuss the use of various temporal knowledge representation formalisms for ontology-mediated query answering over temporal data. In particular, we analyse ontology and query languages based on the linear temporal logic LTL, the multi-dimensional Halpern-Shoham interval temporal logic HSn, as well as the metric temporal logic MTL. Our main focus is on the data complexity of answering temporal ontology-mediated queries and their rewritability into standard first-order and datalog queries

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<) - first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals - its extension FOE with the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies

Temporalised Description Logics for Monitoring Partially Observable Events

Inevitably, it becomes more and more important to verify that the systems surrounding us have certain properties. This is indeed unavoidable for safety-critical systems such as power plants and intensive-care units. We refer to the term system in a broad sense: it may be man-made (e.g. a computer system) or natural (e.g. a patient in an intensive-care unit). Whereas in Model Checking it is assumed that one has complete knowledge about the functioning of the system, we consider an open-world scenario and assume that we can only observe the behaviour of the actual running system by sensors. Such an abstract sensor could sense e.g. the blood pressure of a patient or the air traffic observed by radar. Then the observed data are preprocessed appropriately and stored in a fact base. Based on the data available in the fact base, situation-awareness tools are supposed to help the user to detect certain situations that require intervention by an expert. Such situations could be that the heart-rate of a patient is rather high while the blood pressure is low, or that a collision of two aeroplanes is about to happen. Moreover, the information in the fact base can be used by monitors to verify that the system has certain properties. It is not realistic, however, to assume that the sensors always yield a complete description of the current state of the observed system. Thus, it makes sense to assume that information that is not present in the fact base is unknown rather than false. Moreover, very often one has some knowledge about the functioning of the system. This background knowledge can be used to draw conclusions about the possible future behaviour of the system. Employing description logics (DLs) is one way to deal with these requirements. In this thesis, we tackle the sketched problem in three different contexts: (i) runtime verification using a temporalised DL, (ii) temporalised query entailment, and (iii) verification in DL-based action formalisms