Parsing and Disambiguation of Symbolic Mathematics in the Naproche System

Abstract

Abstract. The Naproche system is a system for linguistically analysing and proof-checking mathematical texts written in a controlled natural language. The aim is to have an input language that is as close as possible to the language that mathematicians actually use when writing textbooks or papers. Mathematical texts consist of a combination of natural language and symbolic mathematics, with symbolic mathematics obeying its own syntactic rules. We discuss the difficulties that a program for parsing and disambiguating symbolic mathematics must face and present how these difficulties have been tackled in the Naproche system. One of these difficulties is the fact that information provided in the preceding contextincluding information provided in natural language -can influence the way a symbolic expression has to be disambiguated.

Towards Mathematical AI via a Model of the Content and Process of Mathematical Question and Answer Dialogues

“…More broadly, "Knowledge Extraction from Text" is a well-known domain of computing research (with workshops running since 2013). The requirements for knowledge extraction from mathematical text, in particular, are being worked out in specialist efforts in linguistics and NLP [13,10,8] (and see in particular the survey in [14]).…”

“…In the current state of the art, discourse structure may have to be laboriously hand-coded. 10 We may be aided in our specific pursuit by the fact that much of mathematics is relatively "formulaic." For example, the first 100 most frequent schematic constructions (like "let X be a Y ") were shown to cover half of the sentences on the detailed but mathematically informal ProofWiki website [18].…”

Modelling the way mathematics is actually done

“…This project was convened by Timothy Gowers in 2009, and he developed 15 rules to address the "questions of procedure" that he anticipated would arise in the project. 15 The basic premise was that people would work together on a shared blog to discuss a given mathematical problem in the open, and jointly work out a solution. Within these ground rules, Gowers carefully explicated the imperative to share comments that are "not fully thought out."…”

“…Sussman gives an example of a LISP program that models "'how to' as well as 'what is'" [66] -namely, a program that he wrote with with Richard Stallman that can replicate the 15 http://gowers.wordpress.com/questions-of-procedure/ 16 http://michaelnielsen.org/polymath1/index.php?title=Main_Page 17 E.g., Footnote 14 draws the data that the Lakatosian framework models from one of the MiniPolymath dialogues, and Rino Nesin tagged two MiniPolymath dialogues into IATC in detail as an initial check on the completeness of the language as it was being developed. 18 http://metameso.org/ar/robotone-example.pdf.…”

“…At the moment, natural language representations of mathematics are largely obscure to text processing techniques, although inroads have been made in understanding the linguistic features of some aspects of mathematics [15,16,21,22]. Mathematical formalisms take this to an extreme, since they simplify and tightly constrain the ways in which their users can write things down.…”