An Algebraic Approach to Learning and Grounding
This work addresses a foundational problem in AI for researchers in symbolic learning and grounding, offering a versatile framework for multiple domains.
The paper tackles the problem of learning semantics of composite algebraic expressions from examples, presenting a framework that simultaneously fills missing algebraic operations and grounds variables to optimize term values, with demonstrated applicability in grammatical inference, picture-language learning, and logic scene grounding.
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 $(\varphi_1, O_1), (\varphi_2, O_2), \ldots$, each consisting of an algebraic term $\varphi_i$ 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 $\varphi_i$ 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.