The field of computational complexity theory is a core theoretical subject in computer science with significant impact also for real-world applications. Although a plethora of individual results are known, a systematic conceptual organisation of this knowledge is still lacking. We propose a modelling approach for creating an ontologically well-founded knowledge base for the theory of computational complexity that will enable storing, querying and reasoning over the vast knowledge of algorithmic problems, complexity classes and their relationships. We determine the core concepts and relations of complexity theory and model them on two levels of approximation: a lightweight version based on the decidable description logic S R O I Q (the underlying formalism of the ontology language OWL 2 DL) and a further extended version based on first-order logic.

Industrial CAD/STEP models provide high-fidelity geometry and product structure, yet automated assembly/disassembly planning also requires machine-interpretable semantics about how parts are connected (e.g., fastening, retention, kinematic guidance) and which operations must precede others. We present an ontology design pattern grounded in DOLCE+DnS Ultralite (DUL) that represents each assembly connection as a reified joint situation, annotated with STEP-derived interface geometry, and optional descriptors such as retention method and degrees of freedom. From these structured connection descriptions, we derive a connection-aware precedence matrix. Hard (MUST) constraints are validated by geometric feasibility checks, while soft (DEFAULT) precedence candidates are generated by reusable templates over joint descriptors and can be overridden when evidence conflicts. A gearbox case study illustrates how coupling-mediated, access-closure, and shaft-mount patterns yield an explainable partial ordering suitable for precedence compilation. The resulting framework complements CAD/STEP with explicit, auditable connection semantics for precedence generation.

This is the second volume of the Special Issue celebrating 10 years of the Joint Ontology Workshops (JOWO). As in the first volume, the second volume includes extended versions of selected papers that were originally presented at JOWO workshops. In this editorial, we moreover offer a retrospective view of the history of the venue, an overview of the variety of topics it has hosted, and an analysis of their evolution over time, reflecting on the development of the community and the diversity of research it has fostered. Together, these elements provide a picture of JOWO as a space where foundational concerns coexist with a broad and expanding range of more applied ontology-related research themes. The papers collected in the two volumes of the Special Issue illustrate both the continuity of core topics and a growing openness towards application-oriented work, as well as the exploratory role of JOWO as a venue for emerging ideas. This editorial thus introduces and situates the contributions in this volume within the broader trajectory of the JOWO community.

Creativity has been a main target of artificial intelligence since its beginning and is still a major challenge today. One well-known option in computational creativity research is conceptual blending where new concepts are created through a selective combination of known ideas. However, existing approaches implementing blending are often either neglecting conceptual aspects, as in image morphing, or they suffer from the high complexity of the creation of the blend. Therefore, we propose a new neuro-symbolic approach to conceptual blending of ontologies based on knowledge graph embeddings which addresses both of these shortcomings. The inherent structure of the embedding space is used both to identify a generic space and to guide the blending process by interpreting blending as path search in the embedding space and by iteratively relaxing the input concepts. This is accomplished by combining a symbolic system for determining a step-wise refinement and analyzing the suitability of these refinements with the help of the embedding. We give an overview on the method and showcase possible heuristics.

In Artificial Intelligence, defeasible reasoning has been studied as one of the key features of common-sense reasoning and consequently various kinds of non-monotonic logics have been developed to model it formally. We recently developed a non-monotonic logic in the Description Logic (DL) framework based on a combination of ideas from prototype theory, weighted DLs (aka "tooth logic"), and earlier work on justifiable exceptions. A central ingredient in the new framework is the notion of a prototype description, weighted characterisations of concepts denoting the typical features of its members. In this paper, we develop an initial ASP translation for this system which allows to reason on instance level queries in the preferred models of a knowledge base. In particular, under reasonable conditions on the form of the input knowledge base, we show that preference reasoning on answer sets can be encoded via standard ASP constructs. We show that the translation is complete with respect to the preferential semantics of our system.

Knowledge base embeddings are a widely applied technique, used for instance to improve link prediction tasks on knowledge graphs by using the geometric regularities occurring during learning. Techniques where ontological concepts are interpreted as boxes have shown to be particularly useful in this context, as they are both suitably expressive and of low computational complexity. However, to use those regularities for learning, it is necessary to determine and understand the possible biases in the approach: how do we distinguish what is learned due to regularities in the data from what is simply based on the representational limitations of the embedding? In this paper, we establish that there are some severe limitations in expressivity when modeling description logic ontologies with box embeddings in intended target languages such as ELHO(o)(perpendicular to). We illustrate that, under some weak assumptions, box semantics always satisfy Helly's Property, and is thus too weak to semantically capture ELHO(o)(perpendicular to) in an adequate way. We then characterize how so-called Helly-satisfiable ELHO(o)(perpendicular to) ontologies can be determined. We discuss the implications of this result with respect to existing box embedding approaches and real-world use cases.

Utilizing abstractions of large conceptual models may enhance their clarity and comprehensibility. This work assesses an existing algorithm for generating abstractions of ontology-driven conceptual models. Although the algorithm has been empirically evaluated using the FAIR catalog of such models, it still lacks formal semantics. This paper addresses this gap by formalizing the basic transformations underlying the abstraction process in 𝒮ℛ𝒪ℐ𝒬 —the expressive and decidable description logic that underpins the Web Ontology Language (OWL 2). Specifically, it demonstrates that, under certain natural assumptions, these transformations are obtained by a formal procedure known as axiom weakening.

Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is, general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, especially characteristic of common-sense contexts. However, it is not easy for a modeller to choose a formalism that is a good fit for a particular domain from an ontological point of view. In this paper, we present a framework for formulating the characteristics of defeasibility and reasoning with exceptions which exploits and incorporates related fields of inquiry, including generics, ceteris paribus laws, and a truthmaking theory for generalisations. The resulting theory allows a grounded comparison of the various formalisms and reveals their ontological commitments. To illustrate and apply this framework, we compare the main systems of non-monotonic logics, showing the differences that may occur from an ontological perspective.

The Joint Ontology Workshops (JOWO) is the flagship venue of the International Association for Ontology and its Applications (IAOA), bringing together workshops that connect the communities of formal and applied ontology with intersecting communities in other fields of knowledge. Since its conception in 2015, JOWO has been held annually, regularly co-locating with the International Conference on Formal Ontology in Information Systems (FOIS). To celebrate its 10th edition, a special edition of the Applied Ontology journal has been organized, welcoming extended versions of papers originally published at JOWO workshops, and with the aim of showcasing the evolutions of high-quality works that originated in this venue. This editorial serves as the preface to the first volume of this two-volume special issue.

Defeasible reasoning has always been a central interest of researchers in the fields of Artificial Intelligence (AI) and Multi-Agent Systems (MAS). In fact, this kind of reasoning is central to dealing with conflicting knowledge or beliefs that agents may hold without causing inconsistencies. In the context of languages for Knowledge Representation, many formal approaches have been proposed specifically in Description Logics (DLs) to deal with this phenomenon. With a perspective towards human-centred and agentive AI and building on the DL paradigm we pursue an approach informed by results coming from fields such as linguistics, philosophy and cognitive science. A central problem in the general area of defeasible DLs is to give a principled solution to the question of where preferences originate from in order to provide a notion of defeasibility. To address this issue, a core aspect of our approach is to compute preferences from the knowledge presented in a knowledge base (with standard semantics) itself. We thus present a non-monotonic DL based on a combination of ideas from prototype theory, weighted DLs (aka ‘tooth logic’), and earlier work on justifiable exceptions. A central ingredient in the new framework is the notion of a prototype description, i.e. weighted characterisations of concepts based on the typical features of its members. We show that through such descriptions it is possible to compute a typicality score which allows to define a preference order over models, useful to solve conflicts across exceptional instances. We define two principle ways of computing such preferences, discuss some core semantic properties and finally outline a translation into Answer Set Programming.

We present an ontology of computational complexity that allows for a representation of research findings on the subject and supports query answering and reasoning tasks to help students and researchers in finding known facts and deriving new ones. The facts about decision problems and complexity classes are organised as a knowledge graph. The relationships between them are axiomatised using the FOWL framework that allows one to combine OWL 2 and first-order logic to balance between reasoning efficiency and expressive power. While the axioms were created through ontological analysis based on received 'textbook knowledge', the facts were extracted from the textual corpus of the 'Complexity Zoo' website, a human-curated 'encyclopedia' of complexity classes, in a human-supervised process employing large language models. We discuss, on the one hand, the modelling choices in relation to the previous work on knowledge representation in mathematics and, on the other hand, the peculiarities of using language models for the mining of complex symbolic facts. Finally, we illustrate some of the features of the hybrid reasoning system by providing a usage example.

Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which is characteristic of common-sense contexts. However, it is not easy for a modeller to choose among these systems the one that better fits its domain from an ontological point of view. In this paper we first propose a framework based on the notions of exceptionality and defeasibility in order to be able to compare formalisms and reveal their ontological commitments. Then, we apply this framework to compare four systems, showing the differences that may occur from an ontological perspective.

Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which is characteristic of common-sense contexts. However, it is not easy for a modeller to choose among these systems the one that better fits its domain from an ontological point of view. In this paper we first propose a framework based on the notions of exceptionality and defeasibility in order to be able to compare formalisms and reveal their ontological commitments. Then, we apply this framework to compare four systems, showing the differences that may occur from an ontological perspective.