Information and Computation - Semantics of Data Types
ACM SIGSAM Bulletin
A Refinement of de Bruijn's Formal Language of Mathematics
Journal of Logic, Language and Information
The Thirteen Books of Euclid's Elements, Books 1 and 2
The Thirteen Books of Euclid's Elements, Books 1 and 2
Restoring Natural Language as a Computerised Mathematics Input Method
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Narrative Structure of Mathematical Texts
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Capturing abstract matrices from paper
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Toward an object-oriented structure for mathematical text
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Spreadsheet Interaction with Frames: Exploring a Mathematical Practice
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
MathLang Translation to Isabelle Syntax
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Dimensions of formality: a case study for MKM in software engineering
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
MathAbs: a representational language for mathematics
Proceedings of the 8th International Conference on Frontiers of Information Technology
Logical structure analysis of scientific publications in mathematics
Proceedings of the International Conference on Web Intelligence, Mining and Semantics
Translating between language and logic: what is easy and what is difficult
CADE'11 Proceedings of the 23rd international conference on Automated deduction
A User-friendly Interface for a Lightweight Verification System
Electronic Notes in Theoretical Computer Science (ENTCS)
Hi-index | 0.00 |
Mathematical texts can be computerized in many ways that capture differing amounts of the mathematical meaning. At one end, there is document imaging, which captures the arrangement of black marks on paper, while at the other end there are proof assistants (e.g., Mizar, Isabelle, Coq, etc.), which capture the full mathematical meaning and have proofs expressed in a formal foundation of mathematics. In between, there are computer typesetting systems (e.g., and Presentation MathML) and semantically oriented systems (e.g., Content MathML, OpenMath, OMDoc, etc.). The MathLang project was initiated in 2000 by Fairouz Kamareddine and Joe Wells with the aim of developing an approach for computerizing mathematical texts and knowledge which is flexible enough to connect the different approaches to computerization, which allows various degrees of formalization, and which is compatible with different logical frameworks (e.g., set theory, category theory, type theory, etc.) and proof systems. The approach is embodied in a computer representation, which we call MathLang, and associated software tools, which are being developed by ongoing work. Three Ph.D. students (Manuel Maarek (2002/2007), Krzysztof Retel (since 2004), and Robert Lamar (since 2006)) and over a dozen master's degree and undergraduate students have worked on MathLang. The project's progress and design choices are driven by the needs for computerizing real representative mathematical texts chosen from various branches of mathematics. Currently, MathLang supports entry of mathematical text either in an XML format or using the editor. Methods are provided for adding, checking, and displaying various information aspects. One aspect is a kind of weak type system that assigns categories (term, statement, noun (class), adjective (class modifier), etc.) to parts of the text, deals with binding names to meanings, and checks that a kind of grammatical sense is maintained. Another aspect allows weaving together mathematical meaning and visual presentation and can associate natural language text with its mathematical meaning. Another aspect allows identifying chunks of text, marking their roles (theorem, definition, explanation, example, section, etc.), and indicating relationships between the chunks (A uses B, A contradicts B, A follows from B, etc.). Software tool support can use this aspect to check and explain the overall logical structure of a text. Further aspects are being designed to allow adding additional formality to a text such as proof structure and details of how a human-readable proof is encoded into a fully formalized version (so far this has only been done for Mizar and started for Isabelle). A number of mathematical texts have been computerized, helping with the development of these aspects, and indicating what additional work is needed for the future. This paper surveys the past and future work of the MathLang project.