A Mathematical Knowledge Base for Proving Theorems in Semigroup and Automata Theory - Part I

Abstract

We present a mathematical knowledge base containing the factual knowledge of the first of three parts of a textbook on semi-groups and automata, namely "P. Deussen: Halbgruppen und Automaten". Like almost all mathematical textbooks this textbook is not self-contained, but there are some algebraic and set-theoretical concepts not being explained. These concepts are added to the knowledge base. Furthermore there is knowledge about the natural numbers, which is formalized following the first paragraph of "E. Landau: Grundlagen der Analysis". The data base is written in a sorted higher-order logic, a variant of POST , the working language of the proof development environment \Omega\Gamma mkrp. We distinguish three different types of knowledge: axioms, definitions, and theorems. Up to now, there are only 2 axioms (natural numbers and cardinality), 149 definitions (like that for a semi-group), and 165 theorems. The consistency of such knowledge bases cannot be proved in general, but inconsis..