Approximating the rank of a homomorphism using a Prolog based system

A system of Prolog based programs for the purpose of approximating the rank of algebraic operations of finite unary algebras is presented. The rank function is a measure of finite algebras and their algebraic operations. Rank is a recursive function used in universal algebra and was first introduced as a tool for proving strong dualizability. Logic programming. particularly Prolog, is commonly used in natural language processing, an area of study devoted to the use of computers to understand human (natural) languages. One goal of this thesis is to explore a relationship between the fields of Mathematics and Computer Science through the application of logic programming techniques on structures from universal algebra. This thesis is motivated by the idea that when universal algebra is viewed as a language, the ideas of natural language processing can be used to create a computer system which approximates rank. The outcome of the research is a computational model that computes the Kth approximation of rank. A set of Prolog programs that act as useful tools on algebraic structures are created.