A Query Language for Formal Mathematical Libraries

TL;DR

This paper introduces QMT, a flexible query language for formal mathematical libraries based on MMT, enabling scalable, cross-library searches without relying on a specific logical formalism.

Contribution

The paper presents QMT, a novel, expressive query language integrated into MMT that supports diverse search paradigms across formalized mathematical knowledge.

Findings

QMT enables integration of various search paradigms.

Implementation provides scalable indexing and querying.

Applicable to multiple mathematical libraries and formats.

Abstract

One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human. Based on the generic representation language MMT, we introduce the mathematical query language QMT: It combines simplicity, expressivity, and scalability while avoiding a commitment to a particular logical formalism. QMT can integrate various search paradigms such as unification, semantic web, or XQuery style queries, and QMT queries can span different mathematical libraries. We have implemented QMT as a part of the MMT API. This combination provides a scalable indexing and query engine that can be readily applied to any library of mathematical knowledge. While our focus here is on libraries that are available in a content markup language, QMT naturally extends to presentation and narration markup languages.