Semi-bracketed contextual grammars

Bracketed and fully bracketed contextual grammars were introduced to bring the concept of a tree structure to the strings by associating a pair of parentheses to the adjoined contexts in the derivation. In this paper, we show that these grammars fail to generate all the basic non-context-free languages, thus cannot be a syntactical model for natural languages. To overcome this failure, we introduce a new class of fully bracketed contextual grammars, called the semi-bracketed contextual grammars, where the selectors can also be non-minimally Dyck covered language. We see that the tree structure to the derived strings is still preserved in this variant. when this new grammar is combined with the maximality feature, the generative power of these grammars is increased to the extend of covering the family of context-free languages and some basic non-context-free languages, thus possessing many properties of the so called `MCS formalism'.