A variety of particular formalizations exist, most of them developed by Edward Stabler, Alain Lecomte, Christian Retoré, or combinations thereof.
Lecomte and Retoré (2001) [1] introduce a formalism that modifies that core of the Lambek Calculus to allow for movement-like processes to be described without resort to the combinatorics of Combinatory categorial grammar.
Differing only slightly in notation from Lecomte and Retoré (2001), we can define a minimalist grammar as a 3-tuple
is a set of "functional" features (which come in two flavors, "weak", denoted simply
is a syntactic type defined recursively as follows: We can now define 6 inference rules: The first rule merely makes it possible to use lexical items with no extra assumptions.
And finally, the last rule implements "movement" by means of assumption elimination.
The last rule can be given a number of different interpretations in order to fully mimic movement of the normal sort found in the Minimalist Program.
That is, we can rephrase the rule as two sub-rules as follows: Another alternative would be to construct pairs in the /E and \E steps, and use the
This would be more in line with the Minimalist Program, given that multiple movements of an item are possible, where only the highest position is "spelled out".
As a simple example of this system, we can show how to generate the sentence who did John see with the following toy grammar: Let