For humans, learning abstract concepts and learning language go hand in hand: we acquire abstract knowledge primarily through linguistic experience, and acquiring abstract concepts is a crucial step in learning the meanings of linguistic expressions. Number knowledge is a case in point: we largely acquire concepts such as seventy-three through linguistic means, and we can only know what the sentence "seventy-three is more than twice as big as thirty-one" means if we can grasp the meanings of its component number words. How do we begin to solve this problem? One approach is to estimate the distribution from which sentences are drawn, and, in doing so, infer the latent concepts and relationships that best explain those sentences. We present early work on a learning framework called Latent Predicate Networks (LPNs) which learns concepts by inferring the parameters of probabilistic context-sensitive grammars over sentences. We show that for a small fragment of sentences expressing relationships between English number words, we can use hierarchical Bayesian inference to learn grammars that can answer simple queries about previously unseen relationships within this domain. These generalizations demonstrate LPNs' promise as a tool for learning and representing conceptual knowledge in language.
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