Mathematics and Logic as Information Compression by Multiple Alignment, Unification and Search

Abstract

This article introduces the conjecture that "mathematics, logic and related disciplines may usefully be understood as information compression (IC) by 'multiple alignment', 'unification' and 'search' (ICMAUS)". As a preparation for the two main sections of the article, concepts of information and information compression are reviewed. Related areas of research are also described including IC in brains and nervous systems, and IC in relation to inductive inference, Minimum Length Encoding and probabilistic reasoning. The ICMAUS concepts and a computer model in which they are embodied are briefly described. The first of the two main sections describes how many of the commonly-used forms and structures in mathematics, logic and related disciplines (such as theoretical linguistics and computer programming) may be seen as devices for IC. In some cases, these forms and structures may be interpreted in terms of the ICMAUS framework. The second main section describes a selection of examples where processes of calculation and inference in mathematics, logic and related disciplines may be understood as IC. In many cases, these examples may be understood more specifically in terms of the ICMAUS concepts.