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Lexicalized Weil-Founded Grammar (LWFG) is a recently developed syntactic-semantic grammar formalism for deep language understanding, which balances expressiveness with provable learnability results. The learnability result for LWFGs assumes that the semantic composition constraints are learnable. In this paper, we show what are the properties and principles the semantic representation and grammar formalism require, in order to be able to learn these constraints from examples, and give a learning algorithm. We also introduce a LWFG parser as a deductive system, used as an inference engine during LWFG induction. An example for learning a grammar for noun compounds is given.