In this paper, we proposed a novel integration of existing techniques in parsing and grammar induction to offer a complete solution for simultaneously modeling grounded language at the sentence and discourse levels.
we used the Earley algorithm to exploit the special structure of our grammars to achieve approximately linear parsing time, introduced a rescaling approach to handle very long input strings, and utilized Variational Bayes for grammar induction to obtain better solutions than the Expectation Maximization algorithm.