Related papers: An Analytic Propositional Proof System on Graphs

Tangle-tree theorems are an important tool in structural graph theory, and abstract separation systems are a very general setting in which tangle-tree theorems can still be formulated and proven. For infinite abstract separation systems, so…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known tree-of-tangles theorems for graphs, matroids and abstract separation systems…

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…

Large language models (LLMs) have shown promise in table Question Answering (Table QA). However, extending these capabilities to multi-table QA remains challenging due to unreliable schema linking across complex tables. Existing methods…

General treebank analyses are graph structured, but parsers are typically restricted to tree structures for efficiency and modeling reasons. We propose a new representation and algorithm for a class of graph structures that is flexible…

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…

We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of…

The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel…

Signal processing on graphs has received a lot of attention in the recent years. A lot of techniques have arised, inspired by classical signal processing ones, to allow studying signals on any kind of graph. A common aspect of these…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…

Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of…

We provide a novel mathematical implementation of tree-adjoining grammars using two combinatorial definitions of graphs. With this lens, we demonstrate that the adjoining operation defines a pre-Lie operation and subsequently forms a Lie…

Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work…

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…

The modular decomposition of a graph is a canonical representation of its modules. Algorithms for computing the modular decomposition of directed and undirected graphs differ significantly, with the undirected case being simpler, and…

The graphoid axioms for conditional independence, originally described by Dawid [1979], are fundamental to probabilistic reasoning [Pearl, 19881. Such axioms provide a mechanism for manipulating conditional independence assertions without…

We investigate the relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix…