Related papers: Construct Graph Logic
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers…
We study question answering over a dynamic textual environment. Although neural network models achieve impressive accuracy via learning from input-output examples, they rarely leverage various types of knowledge and are generally not…
We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We…
Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
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…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the…
Logic reasoning is a significant ability of human intelligence and also an important task in artificial intelligence. The existing logic reasoning methods, quite often, need to design some reasoning patterns beforehand. This has led to an…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…