Temporal Query Answering w.r.t. DL-Lite-Ontologies

Ontology-based data access (OBDA) generalizes query answering in relational databases. It allows to query a database by using the language of an ontology, abstracting from the actual relations of the database. For ontologies formulated in Description Logics of the DL-Lite family, OBDA can be realized by rewriting the query into a classical first-order query, e.g. an SQL query, by compiling the information of the ontology into the query. The query is then answered using classical database techniques. In this report, we consider a temporal version of OBDA. We propose a temporal query language that combines a linear temporal logic with queries over DL-Litecore-ontologies. This language is well-suited for expressing temporal properties of dynamical systems and is useful in context-aware applications that need to detect specific situations. Using a first-order rewriting approach, we transform our temporal queries into queries over a temporal database. We then present three approaches to answering the resulting queries, all having different advantages and drawbacks.This revised version proves that the presented algorithm achieves a bounded history encoding

Graph based management of temporal data

In recent decades, there has been a significant increase in the use of smart devices and sensors that led to high-volume temporal data generation. Temporal modeling and querying of this huge data have been essential for effective querying and retrieval. However, custom temporal models have the problem of generalizability, whereas the extended temporal models require users to adapt to new querying languages. In this thesis, we propose a method to improve the modeling and retrieval of temporal data using an existing graph database system (i.e., Neo4j) without extending with additional operators. Our work focuses on temporal data represented as intervals (event with a start and end time). We propose a novel way of storing temporal interval as cartesian points where the start time and the end time are stored as the x and y axis of the cartesian coordinate. We present how queries based on Allen’s interval relationships can be represented using our model on a cartesian coordinate system by visualizing these queries. Temporal queries based on Allen’s temporal intervals are then used to validate our model and compare with the traditional way of storing temporal intervals (i.e., as attributes of nodes). Our experimental results on a soccer graph database with around 4000 games show that the spatial representation of temporal interval can provide significant performance (up to 3.5 times speedup) gains compared to a traditional model

Evaluation of Temporal Datasets via Interval Temporal Logic Model Checking

The problem of {em temporal dataset evaluation} consists in establishing to what extent a set of temporal data (histories) complies with a given temporal condition. It presents a strong resemblance with the problem of model checking enhanced with the ability of emph{rating} the compliance degree of a model against a formula. In this paper, we solve the temporal dataset evaluation problem by suitably combining the outcomes of model checking an interval temporal logic formula against sets of histories (finite interval models), possibly taking into account domain-dependent measures/criteria, like, for instance, sensitivity, specificity, and accuracy. From a technical point of view, the main contribution of the paper is a (deterministic) polynomial time algorithm for interval temporal logic model checking over finite interval models. To the best of our knowledge, this is the first application of a (truly) interval temporal logic model checking in the area of temporal databases and data mining rather than in the formal verification setting

A Demo of Query Languages for Temporal Databases

Cílem této práce je vytvorit aplikaci pro prepojení odlišních prístupu k temporalním datam. Hlavní myšlenkou je umožniť užívateli práci s použitím jazyka TSQL2 nebo ATSQL bez nutnosti zásahu užívatele do relačního databázového systému. Rovnež tak je součastí práce implementace rozhraní JDBC a demonstrační aplikace pro testovaní temporálních dotazu.The aim of this work is to create an application for interconnect diferrences among temporal databases. The main idea of this project is allow user work with languages TSQL2 and ATSQL without user intervention into relation database system. This work also contain implementation of interface JDBC and demonstration application for testing temporal queries.

Runtime Monitoring of Metric First-order Temporal Properties

We introduce a novel approach to the runtime monitoring of complex system properties. In particular, we present an online algorithm for a safety fragment of metric first-order temporal logic that is considerably more expressive than the logics supported by prior monitoring methods. Our approach, based on automatic structures, allows the unrestricted use of negation, universal and existential quantification over infinite domains, and the arbitrary nesting of both past and bounded future operators. Moreover, we show how to optimize our approach for the common case where structures consist of only finite relations, over possibly infinite domains. Under an additional restriction, we prove that the space consumed by our monitor is polynomially bounded by the cardinality of the data appearing in the processed prefix of the temporal structure being monitored

Literature Review on Temporal, Spatial, and Spatiotermpoal Data Models

This paper reviews papers on temporal databases, spatial databases, and spatio-temporal databases

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

A cookbook for temporal conceptual data modelling with description logic

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models

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