An Algebraic Approach to Learning and Grounding

Abstract

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 (ϕ 1 , O 1 ), (ϕ 2 , O 2 ), . . ., each consisting of an algebraic term ϕ i and a set of objects O i . The objective is to simultaneously fill in the missing algebraic operations in A and ground the variables of every ϕ i in O i , 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.