DatalogMTL extends the classical Datalog language with metric temporal logic (MTL), enabling expressive reasoning over temporal data. While existing reasoning approaches, such as materialisation based and automata based methods, offer soundness and completeness, they lack support for handling efficient dynamic updates, a crucial requirement for real-world applications that involve frequent data updates. In this work, we propose DRedMTL, an incremental reasoning algorithm for DatalogMTL with bounded intervals. Our algorithm builds upon the classical DRed algorithm, which incrementally updates the materialisation of a Datalog program. Unlike a Datalog materialisation which is in essence a finite set of facts, a DatalogMTL materialisation has to be represented as a finite set of facts plus periodic intervals indicating how the full materialisation can be constructed through unfolding. To cope with this, our algorithm is equipped with specifically designed operators to efficiently handle such periodic representations of DatalogMTL materialisations. We have implemented this approach and tested it on several publicly available datasets. Experimental results show that DRedMTL often significantly outperforms rematerialisation, sometimes by orders of magnitude.

In this paper, we tackle the incremental maintenance of Datalog inference materialisation when the rule set can be updated. This is particularly relevant in the context of the Internet of Things and Edge computing where smart devices may need to reason over newly acquired knowledge represented as Datalog rules. Our solution is based on an adaptation of a stratification strategy applied to a dependency hypergraph whose nodes correspond to rule sets in a Datalog program. Our implementation supports recursive rules containing both negation and aggregation. We demonstrate the effectiveness of our system on real and synthetic data.

Materialisation facilitates Datalog reasoning by precomputing all consequences of the facts and the rules so that queries can be directly answered over the materialised facts. However, storing all materialised facts may be infeasible in practice, especially when the rules are complex and the given set of facts is large. We observe that for certain combinations of rules, there exist data structures that compactly represent the reasoning result and can be efficiently queried when necessary. In this paper, we present a general framework that allows for the integration of such optimised storage schemes with standard materialisation algorithms. Moreover, we devise optimised storage schemes targeting at transitive rules and union rules, two types of (combination of) rules that commonly occur in practice. Our experimental evaluation shows that our approach significantly improves memory consumption, sometimes by orders of magnitude, while remaining competitive in terms of query answering time.

Datalog reasoning based on the semina\"ive evaluation strategy evaluates rules using traditional join plans, which often leads to redundancy and inefficiency in practice, especially when the rules are complex. Hypertree decompositions help identify efficient query plans and reduce similar redundancy in query answering. However, it is unclear how this can be applied to materialisation and incremental reasoning with recursive Datalog programs. Moreover, hypertree decompositions require additional data structures and thus introduce nonnegligible overhead in both runtime and memory consumption. In this paper, we provide algorithms that exploit hypertree decompositions for the materialisation and incremental evaluation of Datalog programs. Furthermore, we combine this approach with standard Datalog reasoning algorithms in a modular fashion so that the overhead caused by the decompositions is reduced. Our empirical evaluation shows that, when the program contains complex rules, the combined approach is usually significantly faster than the baseline approach, sometimes by orders of magnitude.

DatalogMTL is an extension of Datalog with metric temporal operators that has found applications in temporal ontology-based data access and query answering, as well as in stream reasoning. Practical algorithms for DatalogMTL are reliant on materialisation-based reasoning, where temporal facts are derived in a forward chaining manner in successive rounds of rule applications. Current materialisation-based procedures are, however, based on a naive evaluation strategy, where the main source of inefficiency stems from redundant computations. In this paper, we propose a materialisation-based procedure which, analogously to the classical seminaive algorithm in Datalog, aims at minimising redundant computation by ensuring that each temporal rule instance is considered at most once during the execution of the algorithm. Our experiments show that our optimised seminaive strategy for DatalogMTL is able to significantly reduce materialisation times.

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity conditions provide sufficient conditions for chase termination. In this paper, we present two novel such conditions--model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA)--that generalise many of the acyclicity conditions known so far in the literature. Materialisation provides the basis for several widely-used OWL 2 DL reasoners.

Materialisation is often used in RDF systems as a preprocessing step to derive all facts implied by given RDF triples and rules. Although widely used, materialisation considers all possible rule applications and can use a lot of memory for storing the derived facts, which can hinder performance. We present a novel materialisation technique that compresses the RDF triples so that the rules can sometimes be applied to multiple facts at once, and the derived facts can be represented using structure sharing. Our technique can thus require less space, as well as skip certain rule applications. Our experiments show that our technique can be very effective: when the rules are relatively simple, our system is both faster and requires less memory than prominent state-of-the-art RDF systems.

Assuming that the emergence of consciousness in artificial minds is possible, those minds will feel the urge to create art. But will we be able to understand it? To answer this question, we need to consider two subquestions: when does the machine become an author of an artwork? And how can we form an understanding of the art that it makes? Empathy, we argue, is the force behind our capacity to understand works of art.

The seminaïve algorithm can be used to materialise all consequences of a datalog program, and it also forms the basis for algorithms that incrementally update a materialisation as the input facts change. Certain (combinations of) rules, however, can be handled much more efficiently using custom algorithms. To integrate such algorithms into a general reasoning approach that can handle arbitrary rules, we propose a modular framework for computing and maintaining a materialisation. We split a datalog program into modules that can be handled using specialised algorithms, and we handle the remaining rules using the seminaïve algorithm. We also present two algorithms for computing the transitive and the symmetric-transitive closure of a relation that can be used within our framework. Finally, we show empirically that our framework can handle arbitrary datalog programs while outperforming existing approaches, often by orders of magnitude.

To efficiently answer queries, datalog systems often materialise all consequences of a datalog program, so the materialisation must be updated whenever the input facts change. Several solutions to the materialisation update problem have been proposed. The Delete/Rederive (DRed) and the Backward/Forward (B/F) algorithms solve this problem for general datalog, but both contain steps that evaluate rules "backwards" by matching their heads to a fact and evaluating the partially instantiated rule bodies as queries. We show that this can be a considerable source of overhead even on very small updates. In contrast, the Counting algorithm does not evaluate the rules "backwards," but it can handle only nonrecursive rules. We present two hybrid approaches that combine DRed and B/F with Counting so as to reduce or even eliminate "backward" rule evaluation while still handling arbitrary datalog programs. We show empirically that our hybrid algorithms are usually significantly faster than existing approaches, sometimes by orders of magnitude.