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This paper argues that certain ontology design problems are profitably addressed by treating ontologies as theories and by defining a set of operations that create new ontologies, including their constraints, out of other ontologies. The…
The ontology engineering process is complex, time-consuming, and error-prone, even for experienced ontology engineers. In this work, we investigate the potential of Large Language Models (LLMs) to provide effective OWL ontology drafts…
We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic…
Psychological research consistently finds that human ratings of words across diverse semantic scales can be reduced to a low-dimensional form with relatively little information loss. We find that the semantic associations encoded in the…
Ontologies play a crucial role in organizing and representing knowledge. However, even current ontologies do not encompass all relevant concepts and relationships. Here, we explore the potential of large language models (LLM) to expand an…
It has been reliably shown that the similarity of word embeddings obtained from popular neural models such as BERT approximates effectively a form of semantic similarity of the meaning of those words. It is therefore natural to wonder if…
In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and clocked type theory, and spatial and cohesive type theory. In this…
We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…
Ontology learning in complex domains, such as life sciences, poses significant challenges for current Large Language Models (LLMs). Existing LLMs struggle to generate ontologies with multiple hierarchical levels, rich interconnections, and…
In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems,…
We present an example of two countable $\omega$-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids -- in other words, no…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
We demonstrate some novel links between entropy and description complexity, a notion referring to the minimal formula length for specifying given properties. Let MLU be the logic obtained by extending propositional logic with the universal…
We study ELI queries (ELIQs) in the presence of ontologies formulated in the description logic DL-Lite. For the dialect DL-LiteH, we show that ELIQs have a frontier (set of least general generalizations) that is of polynomial size and can…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
Large language models (LLMs) have shown significant achievements in solving a wide range of tasks. Recently, LLMs' capability to store, retrieve and infer with symbolic knowledge has drawn a great deal of attention, showing their potential…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…