Type theory with records

Type theory with records is a formal semantics representation framework, using records to express type theory types. It has been used in natural language processing, principally computational semantics and dialogue systems.[1][2]

## Syntax

A record type is a set of fields. A field is a pair consisting of a label and a type. Within a record type, field labels are unique. The witness of a record type is a record. A record is a similar set of fields, but fields contain objects instead of types. The object in each field must be of the type declared in the corresponding field in the record type.[3]

Basic type: [x:Ind]

Object: [x=a]

Ptype: [x:Indcboy:boy(x)y:Indcdog:dog(y)chug:hug(x,y)]

Object: [x=acboy=p1y=bcdog=p2chug=p3]

where a and b are individuals (type Ind), p1 is proof that a is a boy, etc.

## References

1. ↑ Cooper, Robin (2005). "Records and Record Types in Semantic Theory". Journal of Logic and Computation 15 (2): 99–112. doi:10.1093/logcom/exi004.
2. ↑ Cooper, Robin (2010). Type theory and semantics in flux. Handbook of the Philosophy of Science. Volume 14: Philosophy of Linguistics. Elsevier.
3. ↑ R. Cooper. Type theory and language: From perception to linguistic communication. Draft of book chapters available from https://sites.google.com/site/typetheorywithrecords/drafts

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