[1] A generative grammar provides a set of operations such as rewriting, insertion, deletion, movement, or combination, and is interpreted as a definition of the set of all and only the objects that these operations are capable of producing through iterative application.
A model-theoretic grammar simply states a set of conditions that an object must meet, and can be regarded as defining the set of all and only the structures of a certain sort that satisfy all of the constraints.
David E. Johnson and Paul M. Postal introduced the idea of model-theoretic syntax in their 1980 book Arc Pair Grammar.
A structure may deviate only slightly from a theory or it may be highly deviant.
Generative grammars, in contrast "entail a sharp boundary between the perfect and the nonexistent, and do not even permit gradience in ungrammaticality to be represented.