Related papers: Beyond formulas-as-cographs: an extension of Boole…

Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…

Comprehensible neural network explanations are foundations for a better understanding of decisions, especially when the input data are infused with malicious perturbations. Existing solutions generally mitigate the impact of perturbations…

Automata networks are a versatile model of finite discrete dynamical systems composed of interacting entities (the automata), able to embed any directed graph as a dynamics on its space of configurations (the set of vertices, representing…

Reasoning is a fundamental problem for computers and deeply studied in Artificial Intelligence. In this paper, we specifically focus on answering multi-hop logical queries on Knowledge Graphs (KGs). This is a complicated task because, in…

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can…

Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…

Logical reasoning over incomplete knowledge graphs to answer complex logical queries is a challenging task. With the emergence of new entities and relations in constantly evolving KGs, inductive logical reasoning over KGs has become a…

Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the…

In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…

In this paper, we propose an end-to-end graph learning framework, namely Iterative Deep Graph Learning (IDGL), for jointly and iteratively learning graph structure and graph embedding. The key rationale of IDGL is to learn a better graph…

Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…

Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich…

We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…

Graph neural networks (GNNs) are deep learning architectures for machine learning problems on graphs. It has recently been shown that the expressiveness of GNNs can be characterised precisely by the combinatorial Weisfeiler-Leman algorithms…

In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…

Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation…

Knowledge Graphs (KGs) are foundational structures in many AI applications, representing entities and their interrelations through triples. However, triple-based KGs lack the contextual information of relational knowledge, like temporal…

The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…

In this paper, we propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that each GNN can be transformed…

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to…