Related papers: Beyond formulas-as-cographs: an extension of Boole…
This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the…
The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database…
Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…
In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques…
We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal…
While LLMs have emerged as performant architectures for reasoning tasks, their compositional generalization capabilities have been questioned. In this work, we introduce a Compositional Generalization Challenge for Graph-based Commonsense…
Assumption-Based Argumentation (ABA) is a powerful structured argumentation formalism, but exact computation of extensions under stable semantics is intractable for large frameworks. We present the first Graph Neural Network (GNN) approach…
Representation learning on text-attributed graphs (TAGs) has attracted significant interest due to its wide-ranging real-world applications, particularly through Graph Neural Networks (GNNs). Traditional GNN methods focus on encoding the…
Despite incredible progress, many neural architectures fail to properly generalize beyond their training distribution. As such, learning to reason in a correct and generalizable way is one of the current fundamental challenges in machine…
In this paper hypergraph Lambek calculus ($\mathrm{HL}$) is presented. This formalism aims to generalize the Lambek calculus ($\mathrm{L}$) to hypergraphs as hyperedge replacement grammars extend context-free grammars. In contrast to the…
Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still…
Graphs are essential for modeling complex interactions across domains such as social networks, biology, and recommendation systems. Traditional Graph Neural Networks, particularly Message Passing Neural Networks (MPNNs), rely heavily on…
Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a…
The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…
Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and…
Graph Neural Networks (GNNs) are effective for node classification in graph-structured data, but they lack explainability, especially at the global level. Current research mainly utilizes subgraphs of the input as local explanations or…
Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Given an input graph and weights on its vertices, the maximum co-2-plex problem is to find a subset of vertices maximizing the sum of their weights and inducing a graph of degree at most 1. In this article, we analyze polyhedral aspects of…
The paper deals with the interpretability of Graph Neural Networks in the context of Boolean Satisfiability. The goal is to demystify the internal workings of these models and provide insightful perspectives into their decision-making…