We establish a correspondence between (fragments of) TEL◯, a temporal extension of the EL description logic with the LTL operator ◯k, and some specific kinds of formal grammars, in particular, conjunctive grammars (context-free grammars equipped with the operation of intersection). This connection implies that TEL◯ does not possess the property of ultimate periodicity of models, and further leads to undecidability of query answering in TEL◯, closing a question left open since the introduction of TEL◯. Moreover, it also allows to establish decidability of query answering for some new interesting fragments of TEL◯, and to reuse for this purpose existing tools and algorithms for conjunctive grammars.

Time series segmentation is a fundamental task in analyzing temporal data across various domains, from human activity recognition to energy monitoring. While numerous state-of-the-art methods have been developed to tackle this problem, the evaluation of their performance remains critically limited. Existing measures predominantly focus on change point accuracy or rely on point-based metrics such as Adjusted Rand Index (ARI), which fail to capture the quality of the detected segments, ignore the nature of errors, and offer limited interpretability. In this paper, we address these shortcomings by introducing two novel evaluation measures: WARI (Weighted Adjusted Rand Index), a temporal extension of ARI that accounts for the position of segmentation errors, and SMS (State Matching Score), a fine-grained metric that identifies and scores four distinct and fundamental types of segmentation errors while allowing error-specific weighting. We empirically validate WARI and SMS on synthetic and real-world benchmarks, showing that they not only provide a more accurate assessment of segmentation quality but also uncover insights, such as error provenance and type, that are inaccessible with traditional measures.

The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in a most general way. This process may not terminate, and a major problem is to decide whether it does. This problem has been studied for a large number of chase variants, which differ by the conditions under which a rule is applied to extend the database. Surprisingly, the complexity of the universal termination of the restricted (aka standard) chase is not fully understood. We close this gap by placing universal restricted chase termination in the analytical hierarchy. This higher hardness is due to the fairness condition, and we propose an alternative condition to reduce the hardness of universal termination.

This paper addresses one of the fundamental open questions in the realm of existential rules: the conjecture on the finite controllability of bounded derivation depth rule sets (bdd⇒fc). We take a step toward a positive resolution of this conjecture by demonstrating that universal models generated by BDD rule sets cannot contain arbitrarily large tournaments (arbitrarily directed cliques) without entailing a loop query, ∃ E (x,x). This simple yet elegant result narrows the space of potential counterexamples to the (bdd⇒fc) conjecture.

Ontology-based query answering is a problem that takes as input a set of facts F, an ontology R (typically expressed by existential rules), a Boolean query q , and asks whether R and F entails q. This problem is undecidable in general, and a widely investigated approach to tackle it is called query rewriting: from (R,q) (a ``rule query'') is computed q_R such that for any set of facts F, it holds that R and F entail q iff F entails q_R. The literature mostly focused on q_R expressed as a union of conjunctive queries (UCQs), and an algorithm that such a q_R whenever it exists has been proposed in the literature. However, UCQ-rewritability is applicable only in restricted settings. This raises the question whether such a generic algorithm can be designed for a more expressive language, such as datalog. We solve this question by the negative, by studying the difference between datalog-expressibility and datalog-rewritability. In particular, we show that query answering under datalog-expressible rule queries is undecidable.

Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. This paper is an extended abstract of our eponymous publication at KR 2021 where we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argument that this is unavoidable.

Ontology-mediated query answering (OMQA) employs structured knowledge and automated reasoning in order to facilitate access to incomplete and possibly heterogeneous data. While most research on OMQA adopts (unions of) conjunctive queries as the query language, there has been recent interest in handling queries that involve counting. In this paper, we advance this line of research by investigating cardinality queries (which correspond to Boolean atomic counting queries) coupled with DL-Lite ontologies. Despite its apparent simplicity, we show that such an OMQA setting gives rise to rich and complex behaviour. While we prove that cardinality query answering is tractable (TC0) in data complexity when the ontology is formulated in DL-Lite-core, the problem becomes coNP-hard as soon as role inclusions are allowed. For DL-Lite-pos-H (which allows only positive axioms), we establish a P-coNP dichotomy and pinpoint the TC0 cases; for DL-Lite-core-H (allowing also negative axioms), we identify new sources of coNP complexity and also exhibit L-complete cases. Interestingly, and in contrast to related tractability results, we observe that the canonical model may not give the optimal count value in the tractable cases, which led us to develop an entirely new approach based upon exploring a space of strategies to determine the minimum possible number of query matches.

Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are decidable and can only recognize properties that are preserved under homomorphisms. In this paper, we show the converse: every decidable query that is closed under homomorphism can be expressed by an existential rule set for which the standard chase universally terminates. Membership in this fragment is not decidable, but we show via a diagonalisation argument that this is unavoidable.

In this paper, we consider existential rules, an expressive formalism well adapted to the representation of ontological knowledge, as well as data-to-ontology mappings in the context of ontology-based data integration. The chase is a fundamental tool to do reasoning with existential rules as it computes all the facts entailed by the rules from a database instance. We introduce parallelisable sets of existential rules, for which the chase can be computed in a single breadth-first step from any instance. The question we investigate is the characterization of such rule sets. We show that parallelisable rule sets are exactly those rule sets both bounded for the chase and belonging to a novel class of rules, called pieceful. The pieceful class includes in particular frontier-guarded existential rules and (plain) datalog. We also give another characterization of parallelisable rule sets in terms of rule composition based on rewriting.

Ontology-mediated query answering (OMQA) is a promising approach to data access and integration that has been actively studied in the knowledge representation and database communities for more than a decade. The vast majority of work on OMQA focuses on conjunctive queries, whereas more expressive queries that feature counting or other forms of aggregation remain largely unexplored. In this paper, we introduce a general form of counting query, relate it to previous proposals, and study the complexity of answering such queries in the presence of DL-Lite ontologies. As it follows from existing work that query answering is intractable and often of high complexity, we consider some practically relevant restrictions, for which we establish improved complexity bounds.

Existential rules, long known as tuple-generating dependencies in database theory, have been intensively studied in the last decade as a powerful formalism to represent ontological knowledge in the context of ontology-based query answering. A knowledge base is then composed of an instance that contains incomplete data and a set of existential rules, and answers to queries are logically entailed from the knowledge base. This brought again to light the fundamental chase tool, and its different variants that have been proposed in the literature. It is well-known that the problem of determining, given a chase variant and a set of existential rules, whether the chase will halt on any instance, is undecidable. Hence, a crucial issue is whether it becomes decidable for known subclasses of existential rules. In this work, we consider linear existential rules with atomic head, a simple yet important subclass of existential rules that generalizes inclusion dependencies. We show the decidability of the all-instance chase termination problem on these rules for three main chase variants, namely semi-oblivious, restricted and core chase. To obtain these results, we introduce a novel approach based on so-called derivation trees and a single notion of forbidden pattern. Besides the theoretical interest of a unified approach and new proofs for the semi-oblivious and core chase variants, we provide the first positive decidability results concerning the termination of the restricted chase, proving that chase termination on linear existential rules with atomic head is decidable for both versions of the problem: Does every chase sequence terminate? Does some chase sequence terminate?

Data integration systems allow users to access data sitting in multiple sources by means of queries over a global schema, related to the sources via mappings. Datasources often contain sensitive information, and thus an analysis is needed to verify that a schema satisfies a privacy policy, given as a set of queries whose answers should not be accessible to users. Such an analysis should take into account not only knowledge that an attacker may have about the mappings, but also what they may know about the semantics of the sources.In this paper, we show that source constraints can have a dramatic impact on disclosure analysis. We study the problem of determining whether a given data integration system discloses a source query to an attacker in the presence of constraints, providing both lower and upper bounds on source-aware disclosure analysis.

Ontology-mediated query answering is concerned with the problem of answering queries over knowledge bases consisting of a database instance and an ontology. While most work in the area focuses on conjunctive queries, navigational queries are gaining increasing attention. In this paper, we investigate the complexity of answering two-way conjunctive regular path queries (CRPQs) over knowledge bases whose ontology is given by a set of guarded existential rules. We first consider the subclass of linear existential rules and show that CRPQ answering is EXPTIME-complete in combined complexity and NL-complete in data complexity, matching the recently established bounds for answering non-conjunctive RPQs. For guarded rules, we provide a non-trivial reduction to the linear case, which allows us to show that the complexity of CRPQ answering is the same as for plain conjunctive queries, namely, 2EXPTIME-complete in combined complexity and PTIME-complete in data complexity.

Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, i.e., for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it accepts all words over its input alphabet. Deciding universality is \PSpace-complete for poNFAs, and we show that this remains true even when restricting to a fixed alphabet. This is nontrivial since standard encodings of alphabet symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP-complete complexity bound can be obtained if we require that all self-loops in the poNFA are deterministic, in the sense that the symbol read in the loop cannot occur in any other transition from that state. We find that such restricted poNFAs (rpoNFAs) characterise the class of R-trivial languages, and we establish the complexity of deciding if the language of an NFA is R-trivial. Nevertheless, the limitation to fixed alphabets turns out to be essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSPACE-complete. Our results also prove the complexity of the inclusion and equivalence problems, since universality provides the lower bound, while the upper bound is mostly known or proved in the paper.

As the world's affairs get increasingly more digital, timely production and consumption of news require to efficiently and quickly exploit heterogeneous data sources. Discussions with journalists revealed that content management tools currently at their disposal fall very short of expectations. We demonstrate T atooine , a lightweight data integration prototype, which allows to quickly set up integration queries across (very) heterogeneous data sources, capitalizing on the many data links (joins) available in this application domain. Our demonstration is based on scenarios we study in collaboration with Le Monde, France's major newspaper.

Ontology-Based Data Access (OBDA) is a recent paradigm aiming at enhancing data access by taking ontological knowledge into account. When using existential rules as ontological language, query answering is an undecidable problem, whence numerous decidable classes of ontologies have been defined, ranging from classes with very good computational complexities (AC0 in data complexity) to classes with much larger expressivity. However, actually implementable algorithms have been proposed only for very restricted classes (typically those coinciding with lightweight description logics). The aim of this paper is to show how to deal with more expressive ontologies by proposing an algorithm that performs both materialization and rewriting and is applicable for a significant generalization of lightweight description logics. To this end, we first modify an existing algorithm previously proposed for a very generic class of rules, namely greedy bounded treewidth sets of rules. We then exhibit a special case, called pattern oblivious rule sets, which significantly generalizes the ℰℒℋdrdescription logic, which underlies the OWL 2 EL ontology standard, while keeping the beneficial worst-case computational complexity. We last define a subclass of pattern oblivious rules that is recognizable in polynomial time.

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