Metamodeling helps in specifying conceptual modelling requirements with the notion of meta-classes (for instance, classes that are instances of other classes) and meta-properties (relations between metaconcepts). These notions can be expressed in OWL Full. However, OWL Full is so expressive for metamodeling that it leads to undecidability [13]. OWL 2 DL and its sub-profiles guarantee decidability, but they provide a very restricted form of metamodeling [7] and give no semantic support due to the prevalent Direct Semantics (DS). Consider an example adapted from [6], concerning the modeling of biological species, stating that all golden eagles are eagles, all eagles are birds, and Harry is an instance of GoldenEagle, which further can be inferred as an instance of Eagle and Bird. However, in the species domain one can not just express properties of and relationships among species, but also express properties of the species themselves. For example "GoldenEagle is listed in the IUCN Red List of endangered species" states that GoldenEagle as a whole class is an endangered species. Note that this is also not a subclass relation, as Harry is not an endangered species. To formally model this expression, we can declare GoldenEagle to be an instance of new class EndangeredSpecies.

Metamodeling is a general approach to expressing knowledge about classes and properties in an ontology. It is a desirable modeling feature in multiple applications that simplifies the extension and reuse of ontologies. Nevertheless, allowing metamodeling without restrictions is problematic for several reasons, mainly due to undecidability issues. Practical languages, therefore, forbid classes to occur as instances of other classes or treat such occurrences as semantically different objects. Specifically, meta-querying in SPARQL under the Direct Semantic Entailment Regime (DSER) uses the latter approach, thereby effectively not supporting meta-queries. However, several extensions enabling different metamodeling features have been proposed over the last decade. This paper deals with the Metamodeling Semantics (MS) over OWL 2 QL and the Metamodeling Semantic Entailment Regime (MSER), as proposed in Lenzerini et al. (2015) and Lenzerini et al. (2020); Cima et al. (2017). A reduction from OWL 2 QL to Datalog for meta-querying was proposed in Cima et al. (2017). In this paper, we experiment with various logic programming tools that support Datalog querying to determine their suitability as back-ends to MSER query answering. These tools stem from different logic programming paradigms (Prolog, pure Datalog, Answer Set Programming, Hybrid Knowledge Bases). Our work shows that the Datalog approach to MSER querying is practical also for sizeable ontologies with limited resources (time and memory). This paper significantly extends Qureshi & Faber (2021) by a more detailed experimental analysis and more background. Under consideration in Theory and Practice of Logic Programming (TPLP).

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take into account the rank of the solution matrix. This method has applications in feature extraction, matrix column selection, and dictionary learning, and it is distinct from commonly used $\ell_{2,1}$ regularization and other existing regularization-based approaches because it can exploit the full rank of the row-sparse solution matrix, a key feature in many applications. We provide a proof of the method's rank-awareness, establish the existence of solutions to the proposed optimization problem, and develop an efficient algorithm for solving it, whose convergence is analyzed. We also present numerical experiments to illustrate the theory and demonstrate the effectiveness of our method on real-life problems.

Objective: To create a commons for infectious disease (ID) epidemiology in which epidemiologists, public health officers, data producers, and software developers can not only share data and software, but receive assistance in improving their interoperability. Materials and Methods: We represented 586 datasets, 54 software, and 24 data formats in OWL 2 and then used logical queries to infer potentially interoperable combinations of software and datasets, as well as statistics about the FAIRness of the collection. We represented the objects in DATS 2.2 and a software metadata schema of our own design. We used these representations as the basis for the Content, Search, FAIR-o-meter, and Workflow pages that constitute the MIDAS Digital Commons. Results: Interoperability was limited by lack of standardization of input and output formats of software. When formats existed, they were human-readable specifications (22/24; 92%); only 3 formats (13%) had machine-readable specifications. Nevertheless, logical search of a triple store based on named data formats was able to identify scores of potentially interoperable combinations of software and datasets. Discussion: We improved the findability and availability of a sample of software and datasets and developed metrics for assessing interoperability. The barriers to interoperability included poor documentation of software input/output formats and little attention to standardization of most types of data in this field. Conclusion: Centralizing and formalizing the representation of digital objects within a commons promotes FAIRness, enables its measurement over time and the identification of potentially interoperable combinations of data and software.

Ontologies are used in various domains, with RDF and OWL being prominent standards for ontology development. RDF is favored for its simplicity and flexibility, while OWL enables detailed domain knowledge representation. However, as ontologies grow larger and more expressive, reasoning complexity increases, and traditional reasoners struggle to perform efficiently. Despite optimization efforts, scalability remains an issue. Additionally, advancements in automated knowledge base construction have created large and expressive ontologies that are often noisy and inconsistent, posing further challenges for conventional reasoners. To address these challenges, researchers have explored neuro-symbolic approaches that combine neural networks' learning capabilities with symbolic systems' reasoning abilities. In this chapter,we provide an overview of the existing literature in the field of neuro-symbolic deductive reasoning supported by RDF(S), the description logics EL and ALC, and OWL 2 RL, discussing the techniques employed, the tasks they address, and other relevant efforts in this area.

We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conflicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints according to a recently introduced formalism that we also recall. The tool works by translating the standpoint-enhanced version of the description logic SROIQ to its plain (i.e. classical) version. Existing reasoners can then be directly used to provide automated support for reasoning about diverse standpoints.

The tractability of the lightweight description logic EL has allowed for the construction of large and widely used ontologies that support semantic interoperability. However, comprehensive domains with a broad user base are often at odds with strong axiomatisations otherwise useful for inferencing, since these are usually context-dependent and subject to diverging perspectives. In this paper we introduce Standpoint EL, a multi-modal extension of EL that allows for the integrated representation of domain knowledge relative to diverse, possibly conflicting standpoints (or contexts), which can be hierarchically organised and put in relation to each other. We establish that Standpoint EL still exhibits EL's favourable PTime standard reasoning, whereas introducing additional features like empty standpoints, rigid roles, and nominals makes standard reasoning tasks intractable.

In ontology development, there is a gap between domain ontologies which mostly use the web ontology language, OWL, and foundational ontologies written in first-order logic, FOL. To bridge this gap, we present Gavel, a tool that supports the development of heterogeneous 'FOWL' ontologies that extend OWL with FOL annotations, and is able to reason over the combined set of axioms. Since FOL annotations are stored in OWL annotations, FOWL ontologies remain compatible with the existing OWL infrastructure. We show that for the OWL domain ontology OBI, the stronger integration with its FOL top-level ontology BFO via our approach enables us to detect several inconsistencies. Furthermore, existing OWL ontologies can benefit from FOL annotations. We illustrate this with FOWL ontologies containing mereotopological axioms that enable new meaningful inferences. Finally, we show that even for large domain ontologies such as ChEBI, automatic reasoning with FOL annotations can be used to detect previously unnoticed errors in the classification.

Controlled Query Evaluation (CQE) has been recently studied in the context of Semantic Web ontologies. The goal of CQE is concealing some query answers so as to prevent external users from inferring confidential information. In general, there exist multiple, mutually incomparable ways of concealing answers, and previous CQE approaches choose in advance which answers are visible and which are not. In this paper, instead, we study a dynamic CQE method, namely, we propose to alter the answer to the current query based on the evaluation of previous ones. We aim at a system that, besides being able to protect confidential data, is maximally cooperative, which intuitively means that it answers affirmatively to as many queries as possible; it achieves this goal by delaying answer modifications as much as possible. We also show that the behavior we get cannot be intensionally simulated through a static approach, independent of query history. Interestingly, for OWL 2 QL ontologies and policy expressed through denials, query evaluation under our semantics is first-order rewritable, and thus in AC0 in data complexity. This paves the way for the development of practical algorithms, which we also preliminarily discuss in the paper.

We present a novel rewriting technique for conjunctive query answering over OWL 2 QL ontologies. In general, the obtained rewritings are not necessarily correct and can be of exponential size in the length of the query. We argue, however, that in most, if not all, practical cases the rewritings are correct and of polynomial size. Moreover, we prove some sufficient conditions, imposed on queries and ontologies, that guarantee correctness and succinctness. We also support our claim by experimental results.