LIGs have been used in the literature (Weir and Joshi 1988;Vijay-Shanker and Weir 1991) to provide a common framework for the extensions of context-free grammars.
vijay-Shanker and Weir (1991Weir ( , 1993 showed a weak equivalence between LIGs, TAGs, and combinatory categorial grammars (Steedman 2000) and proposed a LIG-based polynomial-time CYK recognition algorithm for TAGs and combinatory categorical grammars.