The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively completes the database as dictated by the constraints. A key challenge, though, is the fact that it may not terminate, which leads to the problem of checking whether it terminates given a database and a set of constraints. In this work, we focus on the semi-oblivious version of the chase, which is well-suited for practical implementations, and linear existential rules, a central class of constraints with several applications. In this setting, there is a mature body of theoretical work that provides syntactic characterizations of when the chase terminates, algorithms for checking chase termination, precise complexity results, and worst-case optimal bounds on the size of the result of the chase (whenever is finite). Our main objective is to experimentally evaluate the existing chase termination algorithms with the aim of understanding which input parameters affect their performance, clarifying whether they can be used in practice, and revealing their performance limitations.

Explaining why a database query result is obtained is an essential task towards the goal of Explainable AI, especially nowadays where expressive database query languages such as Datalog play a critical role in the development of ontology-based applications. A standard way of explaining a query result is the so-called why-provenance, which essentially provides information about the witnesses to a query result in the form of subsets of the input database that are sufficient to derive that result. To our surprise, despite the fact that the notion of why-provenance for Datalog queries has been around for decades and intensively studied, its computational complexity remains unexplored. The goal of this work is to fill this apparent gap in the why-provenance literature. Towards this end, we pinpoint the data complexity of why-provenance for Datalog queries and key subclasses thereof. The takeaway of our work is that why-provenance for recursive queries, even if the recursion is limited to be linear, is an intractable problem, whereas for non-recursive queries is highly tractable. Having said that, we experimentally confirm, by exploiting SAT solvers, that making why-provenance for (recursive) Datalog queries work in practice is not an unrealistic goal.

In this paper, we introduce and illustrate the novel phenomenon of Conceptual Entanglement which emerges due to the representational manifoldness immanent while incrementally modelling domain ontologies step-by-step across the following five levels: perception, labelling, semantic alignment, hierarchical modelling and intensional definition. In turn, we propose Conceptual Disentanglement, a multi-level conceptual modelling strategy which enforces and explicates, via guiding principles, semantic bijections with respect to each level of conceptual entanglement (across all the above five levels) paving the way for engineering conceptually disentangled domain ontologies. We also briefly argue why state-of-the-art ontology development methodologies and approaches are insufficient with respect to our characterization.

For a long time threat modeling was treated as a manual, complicated process. However modern agile development methodologies and cloud computing technologies require adding automatic threat modeling approaches. This work considers two challenges: creating a set of machine-readable data flow diagrams that represent real cloud based applications; and usage domain specific knowledge for automatic analysis of the security aspects of such applications. The set of 180 semantic diagrams (ontologies and knowledge graphs) is created based on cloud configurations (Docker Compose); the set includes a manual taxonomy that allows to define the design and functional aspects of the web based and data processing applications; the set can be used for various research in the threat modeling field. This work also evaluates how ontologies and knowledge graphs can be used to automatically recognize patterns (mapped to security threats) in diagrams. A pattern represents features of a diagram in form of a request to a knowledge base, what enables its recognition in a semantic representation of a diagram. In an experiment four groups of the patterns are created (web applications, data processing, network, and docker specific), and the diagrams are examined by the patterns. Automatic results, received for the web applications and data processing patterns, are compared with the manual taxonomy in order to study challenges of automatic threat modeling. Keywords: threat modeling, data flow diagram, ontologies, knowledge graph, OWL, RDF, SPARQL, DFD.

Business Knowledge Graphs (KGs) are important to many enterprises today, providing factual knowledge and structured data that steer many products and make them more intelligent. Despite their promising benefits, building business KG necessitates solving prohibitive issues of deficient structure and multiple modalities. In this paper, we advance the understanding of the practical challenges related to building KG in non-trivial real-world systems. We introduce the process of building an open business knowledge graph (OpenBG) derived from a well-known enterprise, Alibaba Group. Specifically, we define a core ontology to cover various abstract products and consumption demands, with fine-grained taxonomy and multimodal facts in deployed applications. OpenBG is an open business KG of unprecedented scale: 2.6 billion triples with more than 88 million entities covering over 1 million core classes/concepts and 2,681 types of relations. We release all the open resources (OpenBG benchmarks) derived from it for the community and report experimental results of KG-centric tasks. We also run up an online competition based on OpenBG benchmarks, and has attracted thousands of teams. We further pre-train OpenBG and apply it to many KG- enhanced downstream tasks in business scenarios, demonstrating the effectiveness of billion-scale multimodal knowledge for e-commerce. All the resources with codes have been released at \url{https://github.com/OpenBGBenchmark/OpenBG}.

Automating ontology construction and curation is an important but challenging task in knowledge engineering and artificial intelligence. Prediction by machine learning techniques such as contextual semantic embedding is a promising direction, but the relevant research is still preliminary especially for expressive ontologies in Web Ontology Language (OWL). In this paper, we present a new subsumption prediction method named BERTSubs for classes of OWL ontology. It exploits the pre-trained language model BERT to compute contextual embeddings of a class, where customized templates are proposed to incorporate the class context (e.g., neighbouring classes) and the logical existential restriction. BERTSubs is able to predict multiple kinds of subsumers including named classes from the same ontology or another ontology, and existential restrictions from the same ontology. Extensive evaluation on five real-world ontologies for three different subsumption tasks has shown the effectiveness of the templates and that BERTSubs can dramatically outperform the baselines that use (literal-aware) knowledge graph embeddings, non-contextual word embeddings and the state-of-the-art OWL ontology embeddings.

This paper is devoted to the problems of ontology-based mathematical knowledge management and representation. The main attention is paid to the development of a formal model for the representation of mathematical statements in the Open Linked Data cloud. The proposed model is intended for applications that extract mathematical facts from natural language mathematical texts and represent these facts as Linked Open Data. The model is used in development of a new version of the OntoMath${}^{\mathrm{PRO}}$ ontology of professional mathematics is described. OntoMath${}^{\mathrm{PRO}}$ underlies a semantic publishing platform, that takes as an input a collection of mathematical papers in LaTeX format and builds their ontology-based Linked Open Data representation. The semantic publishing platform, in turn, is a central component of OntoMath digital ecosystem, an ecosystem of ontologies, text analytics tools, and applications for mathematical knowledge management, including semantic search for mathematical formulas and a recommender system for mathematical papers. According to the new model, the ontology is organized into three layers: a foundational ontology layer, a domain ontology layer and a linguistic layer. The domain ontology layer contains language-independent math concepts. The linguistic layer provides linguistic grounding for these concepts, and the foundation ontology layer provides them with meta-ontological annotations. The concepts are organized in two main hierarchies: the hierarchy of objects and the hierarchy of reified relationships.

Once deployed in the real world, autonomous underwater vehicles (AUVs) are out of reach for human supervision yet need to take decisions to adapt to unstable and unpredictable environments. To facilitate research on self-adaptive AUVs, this paper presents SUAVE, an exemplar for two-layered system-level adaptation of AUVs, which clearly separates the application and self-adaptation concerns. The exemplar focuses on a mission for underwater pipeline inspection by a single AUV, implemented as a ROS2-based system. This mission must be completed while simultaneously accounting for uncertainties such as thruster failures and unfavorable environmental conditions. The paper discusses how SUAVE can be used with different self-adaptation frameworks, illustrated by an experiment using the Metacontrol framework to compare AUV behavior with and without self-adaptation. The experiment shows that the use of Metacontrol to adapt the AUV during its mission improves its performance when measured by the overall time taken to complete the mission or the length of the inspected pipeline.

Knowledge plays a critical role in artificial intelligence. Recently, the extensive success of pre-trained language models (PLMs) has raised significant attention about how knowledge can be acquired, maintained, updated and used by language models. Despite the enormous amount of related studies, there still lacks a unified view of how knowledge circulates within language models throughout the learning, tuning, and application processes, which may prevent us from further understanding the connections between current progress or realizing existing limitations. In this survey, we revisit PLMs as knowledge-based systems by dividing the life circle of knowledge in PLMs into five critical periods, and investigating how knowledge circulates when it is built, maintained and used. To this end, we systematically review existing studies of each period of the knowledge life cycle, summarize the main challenges and current limitations, and discuss future directions.

Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete.