The Naproche System

The Naproche project (Natural language Proof Checking) was initiated by Bernhard Schröder and Peter Koepke at the University of Bonn to focus on an interdisciplinary study of the semi-formal language of mathematics. A central goal of Naproche is to develop a controlled natural language (CNL) for mathematical texts and adapted proof checking software which checks texts written in the CNL for syntactical and mathematical correctness. The project is still at a prototypical stage, further information is available at www.naproche.net. This paper describes the Naproche system, an implementation of the ideas developed by the Naproche project. The Naproche system accepts LTEX-style texts, consisting of mathematical formulas imbedded in a controlled natural language. Texts written in the controlled natural language are parsed using techniques from computational linguistics and transformed into first-order formulas. The formulas are given to an automatic theorem prover which checks whether each formula of an argument is a logical consequence of the preceding formulas or axioms.