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.

翻译：我们考虑了从示例中学习复合代数表达式的语义问题。结果是一个用于研究学习任务的多功能框架,可以以下列抽象的形式加以应用:投入是一个部分代数$=alg$,一组有限的示例为$(cvarphi_1,O_1,(\varphi_2,O_2,)\ldots$,每个示例都包含代数术语$\varphi_i$和一组对象~O_i$。目标是同时以$\alg$填补缺失的代数操作,并将每1美元中的变量以$_O$标出,从而使这些术语的总值得到优化。我们通过在语法推理学、图片语言学习和逻辑场景描述的定位方面进行案例研究,来证明这一框架的适用性。