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 $\mathcal{ELHO}(\circ)^\bot$. We illustrate that, under some weak assumptions, box semantics always satisfy Helly’s Property, and is thus too weak to capture semantically $\mathcal{ELHO}(\circ)^\bot$ in an adequate way. We then characterize how so-called Helly-satisfiable $\mathcal{ELHO}(\circ)^\bot$ ontologies can be adequately determined. We discuss the implications of this result with respect to existing box embedding approaches and real-world use cases.

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.

Perceptron operators have been introduced to knowledge representation languages such as description logics in order to define concepts by listing features with associated weights and by giving a threshold. Semantically, an individual then belongs to such a concept if the weighted sum of the listed features it belongs to reaches that threshold. Such operators have been subsequently applied to cognitively-motivated modelling scenarios and to building bridges between learning and reasoning. However, they suffer from the basic limitation that they cannot consider the weight or number of role fillers. This paper introduces an extension of the basic perceptron operator language to address this shortcoming, defining the language ALCP and answering some basic questions regarding the succinctness and complexity of the new language. Namely, we show firstly that in ALCP+, when weights are positive, the language is expressively equivalent to ALCQ, whilst it is strictly more expressive in the general case allowing also negative weights. Secondly, ALCP+ is shown to be strictly more succinct than ALCQ. Thirdly, capitalising on results concerning the logic ALCSCC, we show that despite the added expressivity, reasoning in ALCP remains EXPTIME-complete.

When considering two concepts in terms of extensional logic, their combination will often be trivial, returning an empty extension. Consider e.g. “a Fish Vehicle”, i.e., “a Vehicle which is also a Fish”. Still, people use sophisticated strategies to produce new, non-empty concepts. All these strategies involve the human ability to mend the conflicting attributes of the input concepts and to create new properties of the combination. We focus in particular on the case where a Head concept has superior ‘asymmetric’ control over steering the resulting combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical model of the cognitive and logical mechanics of this asymmetric form of hybridisation. Its implementation is then evaluated using a combination of example ontologies.

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation.

Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, employing the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms.

We discuss steps towards a formalisation of the principles of an agentive naïve proto-physics, designed to match a level of abstraction that reflects the pre-linguistic conceptualisations and elementary notions of agency, as they develop during early human cognitive development. To this end, we present an agentive extension of the multi-dimensional image schema logic ISL based on variants of STIT theory, thus replacing the temporal dimension of ISL with an action-agnostic theory of agency. To begin grasping the notion of ‘animate agent’, we apply the newly defined logic to model the image schematic notion of ‘self movement’ as a means to distinguish the agentive capabilities of a mouse from those of a ball. Finally, we outline the prospects for employing the theory in cognitive robotics.

Parthood is used widely in ontologies across subject domains, specified in a multitude of mereological theories, and even more when combined with topology. To complicate the landscape, decidable languages put restrictions on the language features, so that only fragments of the mereo(topo)logical theories can be represented, even though those full features may be needed to check correctness during modelling. We address these issues by specifying a structured network of theories formulated in multiple logics that are glued together by the various linking constructs of the Distributed Ontology Language, DOL. For the KGEMT mereotopology and its five sub-theories, together with the DL-based OWL species and first- and second-order logic, this network in DOL orchestrates 28 ontologies.

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation of inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures.

We present a computational framework for conceptual blending , a concept invention method that is advocated in cognitive science as a fundamental and uniquely human engine for creative thinking. Our framework treats a crucial part of the blending process, namely the generalisation of input concepts, as a search problem that is solved by means of modern answer set programming methods to find commonalities among input concepts. We also address the problem of pruning the space of possible blends by introducing metrics that capture most of the so-called optimality principles , described in the cognitive science literature as guidelines to produce meaningful and serendipitous blends. As a proof of concept, we demonstrate how our system invents novel concepts and theories in domains where creativity is crucial, namely mathematics and music.

Parthood is used widely in ontologies across subject domains. Some modelling guidance can be gleaned from Ontology, yet it offers multiple mereological theories, and even more when combined with topology, i.e., mereotopology. To complicate the landscape, decidable languages put restrictions on the language features, so that only fragments of the mereo(topo)logical theories can be represented, yet during modelling, those full features may be needed to check correctness. We address these issues by specifying a structured network of theories formulated in multiple logics that are glued together by the various linking constructs of the Distributed Ontology Language, DOL. For the KGEMT mereotopological theory and five sub-theories, together with the DL-based OWL species and first- and second-order logic, this network in DOL orchestrates 28 ontologies. Further, we propose automated steps toward resolution of language feature conflicts when combining modules, availing of the new 'OWL classifier' tool that pinpoints profile violations.

The Distributed Ontology Language DOL, which is currently being standardised as ISO WD 17347 within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3, aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies.

We propose a novel technique for proving the consistency of large, complex and heterogeneous theories for which ‘standard’ automated reasoning methods are considered insufficient. In particular, we exemplify the applicability of the method by establishing the consistency of the foundational ontology DOLCE, a large, first-order ontology. The approach we advocate constructs a global model for a theory, in our case DOLCE, built from smaller models of subtheories together with amalgamability properties between such models. The proof proceeds by (i) hand-crafting a so-called architectural specification of DOLCE which reflects the way models of the theory can be built, (ii) an automated verification of the amalgamability conditions, and (iii) a (partially automated) series of relative consistency proofs.

Using category theoretic notions, in particular diagrams and their colimits, we provide a common semantic backbone for various notions of modularity in structured ontologies, and outline a general approach for representing (heterogeneous) combinations of ontologies through interfaces of various kinds, based on the theory of institutions. This covers theory interpretations, (definitional) language extensions, symbol identifications, and conservative extensions. In particular, we study the problem of inheriting conservativity between sub-theories in a diagram to its colimit ontology, and apply this to the problem of localisation of reasoning in ‘modular ontology languages’ such as DDLs or ℰ-connections.

We aim to combine the semantics of spatial natural language specified as a linguistically motivated ontology, the Generalized Upper Model, with spatial logics or ontologies that specify space according to certain conceptualisations, based on regions, shapes, orientations, distances, or object properties.

We investigate the expressive power and computational properties of two different types of languages intended for speaking about distances. First, we consider a first-order language FM the two-variable fragment of which turns out to be undecidable in the class of distance spaces validating the triangular inequality as well as in the class of all metric spaces. Yet, this two-variable fragment is decidable in various weaker classes of distance spaces. Second, we introduce a variable-free modal language MS that, when interpreted in metric spaces, has the same expressive power as the two-variable fragment of FM. We determine natural and expressive fragments of MS which are decidable in various classes of distance spaces validating the triangular inequality, in particular, the class of all metric spaces.

We introduce a new semantics for modal predicate logic, with respect to which a rich class of first-order modal logics is complete, namely all normal first-order modal logics that are extensions of free quantified K. This logic is defined by combining positive free logic with equality PFL .= and the propositional modal logic K. We then uniformly construct—for each modal predicate logic L—a canonical model whose theory is exactly L. This proves completeness with respect to so-called modalstructures. We add some remarks on canonicity and frame-completeness and finally show that if suitable modal algebras of ‘admissible interpretations’ are added to modal predicate frames, general frame-completeness is gained.