  We present a first attempt to elucidate a theoretical and empirical approach
to design the reward provided by a natural language environment to some
structure learning agent. To this end, we revisit the Information Theory of
unsupervised induction of phrase-structure grammars to characterize the
behavior of simulated actions modeled as set-valued random variables (random
sets of linguistic samples) constituting semantic structures. Our results
showed empirical evidence of that simulated semantic structures (Open
Information Extraction triplets) can be distinguished from randomly constructed
ones by observing the Mutual Information among their constituents. This
suggests the possibility of rewarding structure learning agents without using
pretrained structural analyzers (oracle actors/experts).
