On Exact Learning of Unordered Tree Patterns

Abstract

Tree patterns are natural candidates for representing rules and hypotheses in many tasks such as information extraction and symbolic mathematics. A tree pattern is a tree with labeled nodes where some of the leaves may be labeled with variables, whereas a tree instance has no variables. A tree pattern matches an instance if there is a consistent substitution for the variables that allows a mapping of subtrees to matching subtrees of the instance. A finite union of tree patterns is called a forest. In this paper, we study the learnability of tree patterns from queries when the subtrees are unordered. The learnability is determined by the semantics of matching as defined by the types of mappings from the pattern subtrees to the instance subtrees. We first show that unordered tree patterns and forests are not exactly learnable from equivalence and subset queries when the mapping between subtrees is one-to-one onto, regardless of the computational power of the learner. Tree and forest patterns are learnable from equivalence and membership queries for the one-to-one into mapping. Finally, we connect the problem of learning tree patterns to inductive logic programming by describing a class of tree patterns called Clausal trees that includes non-recursive single-predicate Horn clauses and show that this class is learnable from equivalence and membership queries.