A Language Engineering Architecture for Processing Informal Mathematical Discourse

We present a modular architecture for processing informal mathematical language as found in textbooks and mathematical publica- tions. We point at its properties relevant in addressing three aspects of informal mathematical discourse: (i) the interleaved symbolic and natu- ral language, (ii) the linguistic, domain, and notational context, and (iii) the imprecision of the informal language. The objective in the modular approach is to enable parameterisation of the system with respect to the natural language of the text and the mathematical domain of discourse. Informal mathematical discourse in textbooks and mathematical publications is partly written in natural language and partly in a symbolic notation—even within a single utterance. Be it information retrieval or text mining mathematical documents, flexible human-oriented mathematical user interfaces, or automated verification of informal proofs crucially rely on automated analysis of the informal language. In (8,9,2) we presented methods of, respectively: parsing, lexical analysis, and domain-specific interpretation of informal mathematical proofs, and introduced linguistic resources necessary for processing. In this paper, we present a modular architecture of a system for processing mathematical language based on those resources and emphasise three core aspects of the informal mathematical discourse it addresses: the interleaved symbolic and natural language, the linguistic, domain, and notational context, and the imprecision of the informal language. The objective in the modular approach is to enable parameterisation of the system with respect to the natural language of the text in question, the mathematical domain of the discourse, and the mathematical notation. We first briefly discuss the above-mentioned aspects of the mathematical language based on example utterances, then we present our processing architecture, and finally outline the related work on mathematical discourse and our further work.