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 $\alg$ and a finite set of examples $({\phi }_1,O_1),({\phi }_2,O_2),\dots$, each consisting of an algebraic term ${\phi }_i$ and a set of objects~$O_i$. The objective is to simultaneously fill in the missing algebraic operations in $\alg$ and ground the variables of every ${\phi }_i$ 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.

arXiv commentAccepted to LearnAut 2022 at ICALP 2022