For the current synchronous grammars based SMT, to some extent, the generalization ability of the grammar rules (the usability of the rules for the new sentences) can be considered as a kind of the generative power of the grammar and the disam-biguition ability to the rule candidates can be considered as an embodiment of expressive power.
the generalization ability and the disambiguition ability often contradict each other in practice such that various grammar formalisms in SMT are actually different trade-off between them.