Related papers: GraATP: A Graph Theoretic Approach for Automated T…
The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This…
When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FSTRA). As such, it can be used as an automated theorem prover (ATP) for this theory. {log} is able to automatically…
Graph data is ubiquitous in academia and industry, from social networks to bioinformatics. The pervasiveness of graphs today has raised the demand for algorithms that can answer various questions: Which products would a user like to…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graphs link prediction has been limited due to their computational inefficiency. A new RNNNTP method is proposed in this paper, using a…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Explaining Graph Neural Networks predictions to end users of AI applications in easily understandable terms remains an unsolved problem. In particular, we do not have well developed methods for automatically evaluating explanations, in ways…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a conjecture in a proof assistant. In this work, we introduce several novel concepts and capabilities to address…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Graphs play an important role in many applications. Recently, Graph Neural Networks (GNNs) have achieved promising results in graph analysis tasks. Some state-of-the-art GNN models have been proposed, e.g., Graph Convolutional Networks…
We present an explanation system for applications that leverage Answer Set Programming (ASP). Given a program P, an answer set A of P, and an atom a in the program P, our system generates all explanation graphs of a which help explain why a…
Hypothesis testing is a statistical method used to draw conclusions about populations from sample data, typically represented in tables. With the prevalence of graph representations in real-life applications, hypothesis testing in graphs is…