We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated queries answering which can be done in AC0, NC1, L, NL, P, and coNP for data complexity, provide their rewritings to first-order logic and its extensions with primitive recursion, transitive closure or datalog, and establish lower complexity bounds.

DatalogMTL is an extension of Datalog with operators from metric temporal logic which has received significant attention in recent years. It is a highly expressive knowledge representation language that is well-suited for applications in temporal ontology-based query answering and stream processing. Reasoning in DatalogMTL is, however, of high computational complexity, making implementation challenging and hindering its adoption in applications. In this paper, we present a novel approach for practical reasoning in DatalogMTL which combines materialisation (a.k.a. forward chaining) with automata-based techniques. We have implemented this approach in a reasoner called MeTeoR and evaluated its performance using a temporal extension of the Lehigh University Benchmark and a benchmark based on real-world meteorological data. Our experiments show that MeTeoR is a scalable system which enables reasoning over complex temporal rules and datasets involving tens of millions of temporal facts.

In this paper, we present a program designed to successfully and autonomously play Angry Birds which attempts to embrace motives of human players in their choices of targets they want to shoot at in a game play. The program comprises two modules: the representation module and the reasoning module. In the former we introduce qualitative space representation that utilises notions such as "to lie on", "to lie to the right", "to be a shelter of a target", etc. The latter investigates how particular blocks of a structure behave once one of them has been hit. It includes two algorithms, namely Vertical Impact and Horizontal Impact. The first one is a novel method of investigating the behaviour of complex structures after one of their constituent blocks gets hit. Namely, it predicts which elements of a structure fall if a supporting block gets destroyed. Horizontal Impact, on the other hand, simulates force propagation between adjacent elements after one of them gets struck. We also describe experimental tests we have conducted in which Vertical Impact correctly predicted which blocks will fall in over 98% of investigated cases.

We study DatalogMTL—an extension of Datalog with metric temporal operators—under integer semantics, where the temporal domain of both interpretations and temporal operators consists of integer time points only. This is in contrast to the standard semantics, which is defined over the rational timeline. DatalogMTL under integer semantics is an interesting KR language: on the one hand, one can often assume the integer timeline in applications; on the other hand, it captures prominent temporal extensions of Datalog such as Datalog1S. We show that the choice of integer semantics leads to more favourable computational properties. We first show that reasoning over integers is at most as hard as reasoning over rationals for DatalogMTL and its natural fragments. Then, we investigate fragments of DatalogMTL where adopting the integer semantics makes reasoning easier. In particular, we show that complexity drops from P-hard to NC1-complete for the propositional fragment (where all object variables are grounded), and from TC0-hard to ACC0 for the linear fragment where the past diamond operator is the only metric operator allowed in rule bodies. Thus, reasoning in such fragments is both tractable and highly parallelisable, which suggests their appropriateness for data-intensive applications.