The generalized constraint language and standard constraint language

A concept which has a position of centrality in GTU is that of generalized constraint language (GCL). Informally, GCL is the set of all generalized constraints together with the rules governing syntax, semantics, and generation. Simple examples of elements of GCL are:

(X is small) is likely,

((X, Y) isp A) л (X is B),

(X isp A) л ((X, Y) isv B),

Proj_{Y}((X is A) л (X, Y) isp B),

where л is conjunction. A very simple example of a semantic rule is:

where u and v are generic values of X, Y; and m_{A} and m_{B} are the membership functions of A and B, respectively.

In principle, GCL is an infinite set. However, in most applications only a small subset of GCL is likely to be needed.

A key idea which underlies NL-computation is embodied in the meaning postulate—a postulate which asserts that the meaning of a proposition, p, drawn from a natural language is representable as a generalized constraint. In the context of GCL, the meaning postulate asserts that p may be precisiated through translation into GCL. Transparency of translation may be enhanced through annotation. Simple example of annotation,

In GTU, the set of all standard constraints together with the rules governing syntax, semantics, and generation constitute the standard constraint language (SCL). SCL is a subset of GCL.