The language of mathematics. A linguistic and philosophical investigation
type: Item
instance of: scholarly article
title: The language of mathematics. A linguistic and philosophical investigation
zbMATH Open document ID: 1271.03004
DOI: 10.1007/978-3-642-37012-0
author: Mohan Ganesalingam
published in: Lecture Notes in Computer Science
publication date: 2013-03-07T00:00:00Z
review text: From a linguistic perspective the author analyses several sentences used in mathematical texts and papers (written in English) as those of a certain particular natural language, namely, the language of mathematics, one of whose objectives is to provide a parser for it. There are very few and limited previous studies of this kind: the works of Ranta deal with those of certain specific theories (such as arithmetic, for example) by a linguistic approach, and those of de Bruijn are motivated by an interest coming from computer science more strongly. On the other hand, the subject of this book is a language supposed to cover all mathematical theories. Referring to the observations due to Ranta, the analysis is carried out based on a context-free generative grammar syntactically and discourse representation theory semantically. Some particular characteristics of the language are featured first; for example, the mixture of textual and symbolic expressions. It is also emphasized that for the language to cover all mathematical theories, its grammar needs to satisfy a requirement called `adaptivity', or roughly, to enjoy a mechanism in itself to produce a new term or notation according to a given definition (so that its lexicon cannot be given manually but needs to be open). Then, the main part of the discussion is devoted to the disambiguation problem, for which on symbolic statements in particular it is necessary to categorize the symbols to be used in certain types. But the problem is more complicated than in the case of formal languages because the ambiguity of a sentence containing both textual and symbolic expressions comes from both aspects depending on each other. Therefore, the mechanism for disambiguation is required so as to cover both aspects uniformly. Thus, taking account of the above-mentioned adaptivity as well, the author introduces a new system of type inference, and proposes a typed parsing system based on it. It is also pointed out that the analysis brings…
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 00-02
Mathematics Subject Classification ID: 68-02
Mathematics Subject Classification ID: 00A30
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B65
Mathematics Subject Classification ID: 68Q42
Mathematics Subject Classification ID: 68T50
zbMATH DE Number: 6142694
zbMATH Keywords: the language of mathematics
zbMATH Keywords: context-free generative grammar
zbMATH Keywords: discourse theory
zbMATH Keywords: type inference system
zbMATH Keywords: typed parsing system
Wikidata QID: Q61458335
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-37012-0
OpenAlex ID: W4251347492
description: scientific article; zbMATH DE number 6142694