Related papers: An Analytic Propositional Proof System on Graphs

Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…

In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…

The state-of-the-art models for coreference resolution are based on independent mention pair-wise decisions. We propose a modelling approach that learns coreference at the document-level and takes global decisions. For this purpose, we…

This work bridges the gap between distributed and centralised models of computing in the context of sublinear-time graph algorithms. A priori, typical centralised models of computing (e.g., parallel decision trees or centralised local…

Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…

Textual logical reasoning, especially question-answering (QA) tasks with logical reasoning, requires awareness of particular logical structures. The passage-level logical relations represent entailment or contradiction between propositional…

The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…

In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They…

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…

In this note we introduce a notion of a morphism between two hyperbolic iterated function systems. We prove that the graph of a morphism is the attractor of an iterated function system, giving a Closed Graph Theorem, and show how it can be…

Understanding the decisions of tree-based ensembles and their relationships is pivotal for machine learning model interpretation. Recent attempts to mitigate the human-in-the-loop interpretation challenge have explored the extraction of the…

The group structure on the rational points of elliptic curves plays several important roles, in mathematics and recently also in other areas such as cryptography. However, the famous proofs for the group property (in particular, for its…

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…