On Building a Knowledge Base for Stability Theory

TL;DR

This paper explores the development of a specialized knowledge base for stability theory in electrical engineering, highlighting the gaps in existing repositories and emphasizing the need for detailed, domain-specific mathematical knowledge.

Contribution

It presents an example formalization in Mizar for stability theory, analyzing the specific knowledge required and its presence in current mathematical repositories.

Findings

Existing repositories lack detailed stability theory knowledge

Formalization in Mizar reveals knowledge gaps

Highlights need for domain-specific mathematical repositories

Abstract

A lot of mathematical knowledge has been formalized and stored in repositories by now: different mathematical theorems and theories have been taken into consideration and included in mathematical repositories. Applications more distant from pure mathematics, however --- though based on these theories --- often need more detailed knowledge about the underlying theories. In this paper we present an example Mizar formalization from the area of electrical engineering focusing on stability theory which is based on complex analysis. We discuss what kind of special knowledge is necessary here and which amount of this knowledge is included in existing repositories.