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We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H the problem is either NP-complete, NL-complete, L-complete or is…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…
Whether it be source code in a programming language, prose in natural language, or otherwise, text is highly structured. Currently, text visualizations are confined either to _flat, line-based_ decorations, which can convey only limited…
Architecture styles characterise families of architectures sharing common characteristics. We have recently proposed configuration logics for architecture style specification. In this paper, we study a graphical notation to enhance…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
The advancement of large language models (LLMs) for real-world applications hinges critically on enhancing their reasoning capabilities. In this work, we explore the reasoning abilities of large language models (LLMs) through their…
Academic question answering (QA) in heterogeneous scholarly networks presents unique challenges requiring both structural understanding and interpretable reasoning. While graph neural networks (GNNs) capture structured graph information and…
We focus on a conversational question answering task which combines the challenges of understanding questions in context and reasoning over evidence gathered from heterogeneous sources like text, knowledge graphs, tables, and infoboxes. Our…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
The contribution of this paper is to provide a semantic model (using soft constraints) of the words used by web-users to describe objects in a language game; a game in which one user describes a selected object of those composing the scene,…
Our research integrates graph data with Large Language Models (LLMs), which, despite their advancements in various fields using large text corpora, face limitations in encoding entire graphs due to context size constraints. This paper…
Integrating large language models (LLMs) with knowledge graphs derived from domain-specific data represents an important advancement towards more powerful and factual reasoning. As these models grow more capable, it is crucial to enable…
Training on large-scale graphs has achieved remarkable results in graph representation learning, but its cost and storage have raised growing concerns. As one of the most promising directions, graph condensation methods address these issues…
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…
Understanding the uncertainty in large language model (LLM) explanations is important for evaluating their faithfulness and reasoning consistency, and thus provides insights into the reliability of LLM's output regarding a question. In this…
We consider the recommendations of the World Wide Web Consortium (W3C) about the Resource Description Framework (RDF) and the associated query language SPARQL. We propose a new formal framework based on category theory which provides clear…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…