Abstract: Stream Reasoning is an emerging research area focused on deriving timely and actionable insights from high-velocity, continuously evolving data. It sits at the intersection of Artificial Intelligence and Stream Processing, with strong foundations in Knowledge Representation and Reasoning. Applications span domains such as the Internet of Things, real-time monitoring, social media analytics, and financial event processing. In this talk, I will introduce our work on RDF Stream Processing, a subfield of Stream Reasoning which connects Semantic Web with stream processing technologies. I will present current research activities at the Stream Intelligence Lab (KU Leuven, Campus Kortrijk), including our new reasoning engine, Kolibrie, designed for expressive and efficient reasoning over data streams. I will also discuss ongoing challenges and research directions such as managing inconsistency, incremental materialization, and reasoning on dynamic knowledge graphs.

A knowledge base is a database together with an ontology, which contains rules that can be used to infer new facts not explicitly present in the data. In the general case, this fact-generating procedure can run forever, creating infinitely many versions of the original database of possibly infinite size. When answering queries, all these possible worlds must be considered when computing the result. This version of query answering is called “query entailment”. More formally, we say that a query is entailed by a database if it is true in all of its extensions. To bring query entailment closer to database theory-style query answering, where the data is always finite, a finite version of query entailment has been considered for many classes of queries and rule languages. In the context of “finite query entailment”, a query is said to be entailed by a database if it is true in all of its finite extensions. Unfortunately, this finite semantics can lead to a loss of intended meaning, creating nonsensical databases that do not correspond to the user’s intuition. In this talk, I will introduce a new partially finite semantics, and its corresponding “partially finite query entailment” problem, that aims to reduce the disparity described above by allowing users to choose which part of the data must remain finite. I will show how the problem differs from its unrestricted and finite variants, and that it does not cause an increase in computational complexity, for the logic S. The talk will contain an introduction to the query entailment formalism and should be accessible to those without a background in Description Logics/Knowledge representation.

In this talk, we consider the task of representing the set of all homomorphisms between two finite relational structures by tractable circuit classes from knowledge compilation. The idea is that this may allow us to greatly compress the set, while still allowing us to perform various algorithmic tasks — such as counting and enumeration — efficiently. This is a very general problem which can alternatively be viewed as representing the answers to a CSP or as the result of a full conjunctive query on a relational database. Because of this the problem is in general intractable, we are interested in which restrictions of the problem become tractable. In particular, we are interested in left-hand-side restrictions: for which classes of structures C, is it the case that for every A in C and every B, the set of homomorphisms from A to B has a ‘small’ tractable circuit. I will discuss various results related to this problem. The talk is based on joint work with Christoph Berkholz.

Abstract: In Complex Event Processing (CEP), queries are evaluated over sequential data to recognize specific event patterns. Core features of CEP query languages include sequencing and correlation, the latter being closely related to join operations in relational databases. By slightly shifting perspective, evaluating a join query over sequential (i.e., time-ordered) data can be seen as query evaluation under updates, - a topic studied both in the Database Systems community (under Incremental View Maintenance, or IVM) and in the Database Theory community (under conjunctive queries with updates). In this talk, we’ll explore the connections between CEP, IVM, and conjunctive queries with updates. Building on these links, I’ll introduce a new query model: Conjunctive Queries with Insertion Order (CQ+IO) — a natural extension of conjunctive queries to event streams. This model lies at the intersection of CEP, IVM, and database theory. We investigate the expressive power of CQ+IO by characterizing the class of CQ+IO that can be translated into the automata model proposed for CEP by Pinto et al. (2025), and the class of CQ+IO that can be evaluated using the General Dynamic Yannakakis framework developed by Idris et al. (2020). Interestingly, these two classes intersect — laying the groundwork for transferring ideas and techniques between these previously separate fields.

This talk aims to advertise a new method for factorising words with respect to a finite monoid. The approach lets us represent a word as a tree of bounded size relative to the monoid, where long sequences of contiguous factors that induce the same effect in the monoid are abstracted by retaining only the first and last few. In the case of transition monoids, the size of this tree is polynomially bounded in terms of the size of the monoid. We will explore three a priori unrelated problems and show how they are connected to one another and to the short-ends factorisation method. The talk will focus on presenting those connections rather than describing the solutions. The first problem concerns the parameterised control of populations of MDPs. The second is the sequential flow problem, which asks whether it is possible to compose sequences of graph fragments in order to generate graphs with unbounded flow. The third problem is the computation of the subword closure of the language generated by an indexed grammar. For each of these problems, we establish optimal bounds.