An Algebraic Approach to Learning and Grounding
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We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial algebra A and a finite set of samples (ϕ1, O1), (ϕ2, O2), ..., each consisting of an algebraic term ϕi and a set of objects Oi. The objective is to simultaneously fill in the missing algebraic operations in A and ground the variables of every ϕi in Oi, so that the combined value of the terms is optimised. We demonstrate the applicability of this framework through case studies in grammatical inference, picture-language learning, and the grounding of logic scene descriptions.
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