We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that classify a set of positively- and negatively-labeled structures. We give algorithms for realizability and synthesis of such formulas along with upper and lower bounds. We also establish positive results using our technique for other logics and variants of the learning problem, including first-order logic with least fixed point definitions, higher-order logics, and synthesis of queries and terms with recursively-defined functions.

翻译：我们考虑在有限的可变逻辑中对公式和术语进行语法限制的精确学习,我们提出一种新颖和多功能的自动化理论技术来解决这类问题。我们首先展示了将一套正面和负标签结构分类的学习公式的结果。我们给出了这些公式的可变性和综合的算法,以及上下界和下界。我们还利用我们的其他逻辑和学习问题变式,包括定点定义最低的一阶逻辑、高阶逻辑,以及查询和术语与连带定义功能的合成,取得了积极的结果。