# Mathematical Vernacular and Conceptual Well-Formedness in Mathematical Language

@inproceedings{Luo1997MathematicalVA, title={Mathematical Vernacular and Conceptual Well-Formedness in Mathematical Language}, author={Zhaohui Luo and Paul Callaghan}, booktitle={LACL}, year={1997} }

This paper investigates the semantics of mathematical concepts in a type theoretic framework with coercive subtyping. The typetheoretic analysis provides a formal semantic basis in the design and implementation of Mathematical Vernacular (MV), a natural language suitable for interactive development of mathematics with the support of the current theorem proving technology.
The idea of semantic well-formedness in mathematical language is motivated with examples. A formal system based on a…

## 26 Citations

### Object languages in a type-theoreticmeta-frameworkPaul

- Computer Science
- 2001

Techniques for providing a convenient syntax for object languages implemented via a type-theoretic Logical Framework, and reports on work in progress are presented.

### Coercive Subtyping

- Computer ScienceJ. Log. Comput.
- 1999

This approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, the meaning of an object being in a supertype is given by coercive deenition rules for the deenitional equality.

### Mathematical Vernacular in Type Theory-based Proof Assistants

- Computer Science
- 1998

The Durham Mathematical Vernacular (MV) project is presented, the general design of a prototype to support experimentation with issues of MV is discussed, current work on the prototype is explained, and a prototype is demonstrated at the conference.

### Computer-Assisted Reasoning with Natural Language: Implementing a Mathematical Vernacular

- Computer Science
- 2007

The Durham Mathematical Vernacular project is presented, namely the issue of semantic well-formedness in mathematical descriptions, and a prototype being developed to experiment with aspects of the project.

### Weak Type Theory : a formal language for mathematics

- Linguistics, Computer Science
- 2002

A formal language for expressing mathematics, called Weak Type Theory (‘WTT’), which is close to the usual way in which mathematicians express themselves in writing and has a high degree of reliability in the sense that it gives a true image of what the mathematician intends to say.

### Vernacular Mathematics, Discourse Representation, and Arbitrary Objects

- Philosophy
- 2007

This paper discusses some of the issues that have to be addressed for a systematic treatment of vernacular mathematics. In vernacular proofs, variable letters are introduced and used in a way that…

### An Implementation of LF with Coercive Subtyping & Universes

- Computer ScienceJournal of Automated Reasoning
- 2004

It is claimed that the combination of Tarski-style universes together with coercive subtyping provides an ideal formulation of universes that is both semantically clear and practical to use.

### Understanding informal mathematical discourse

- Computer Science, Mathematics
- 2004

This thesis aims to provide a general framework as well as an implementation for such a proof engine that is capable of processing mathematical proofs automatically, at least with regard to translating the mathematicians’ expert language into the system's artificial formal language.

### Flexible Encoding of Mathematics on the Computer

- Computer Science, MathematicsMKM
- 2004

This paper reports on refinements and extensions to the MathLang framework that add substantial support for natural language text. We show how the extended framework supports multiple views of…

### Coercion completion and conservativity in coercive subtyping

- MathematicsAnn. Pure Appl. Log.
- 2001

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