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'''Type theory with records''' is a formal semantics representation framework, using ''[[Record (logic)|records]]'' to express [[type theory]] ''types''. It has been used in [[natural language processing]], principally [[computational semantics]] and [[dialogue systems]].<ref>Cooper, Robin (2005). ''Records and Record Types in Semantic Theory''. Journal of Logic and Computation. DOI: 10.1093/logcom/exi004</ref><ref>Cooper, Robin (2010). ''Type theory and semantics in flux''. ''Handbook of the Philosophy of Science. Volume 14: Philosophy of Linguistics''. Elsevier.</ref>

== 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.<ref>R. Cooper. Type theory and language: From perception to linguistic communication. Draft of book chapters available from https://sites.google.com/site/typetheorywithrecords/drafts</ref>

Basic type: <math>\begin{bmatrix} \text{x} : Ind \end{bmatrix}</math>

Object: <math>\begin{bmatrix}
\text{x} = a
\end{bmatrix}</math>

Ptype: <math>\left [ \begin{array}{lll}
\text{x} & : & Ind \\
\text{c}_\text{boy} & : & boy(\text{x}) \\
\text{y} & : & Ind \\
\text{c}_\text{dog} & : & dog(\text{y}) \\
\text{c}_\text{hug} & : & hug(x,y)
\end{array} \right ]</math>

Object: <math>\left [ \begin{array}{lll}
\text{x} & = & a \\
\text{c}_\text{boy} & = & p_1 \\
\text{y} & = & b \\
\text{c}_\text{dog} & = & p_2 \\
\text{c}_\text{hug} & = & p_3
\end{array} \right ]</math>

where <math>a</math> is an individiual, <math>p_1</math> is proof that <math>a</math> is a boy, etc.

== References ==
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