A new viewpoint of the G\"odel's incompleteness theorem and its applications

TL;DR

This paper presents a novel perspective on G"odel's incompleteness theorem, exploring its connection to logic and computation, and introduces algorithms and neural network approaches to proof search.

Contribution

It offers a new viewpoint linking logic and computation, along with algorithms for proof search and neural network methods to enhance mathematical proof discovery.

Findings

Reveals a deep relationship between logic and computation.

Provides an algorithm for proof search in first-order logic.

Proposes neural network approaches to improve proof searching.

Abstract

A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a proof of statement in first order logic from finite concrete examples, and an approach be proposed to improve searching mathematical proof by neural network.