Learning Closed Horn Expressions

Abstract

The paper studies the learnability of Horn expressions within the framework of learning from entailment , where the goal is to exactly identify some pre-fixed and unknown expression by making queries to membership and equivalence oracles. It is shown that a class that includes both range restricted Horn expressions (where terms in the conclusion also appear in the condition of a Horn clause) and constrained Horn expressions (where terms in the condition also appear in the conclusion of a Horn clause) is learnable. This extends previous results by showing that a larger class is learnable with better complexity bounds. A further improvement in the number of queries is obtained when considering the class of Horn expressions with inequalities on all syntactically distinct terms.