Learning Definite Horn Formulas from Closure Queries
This work addresses a theoretical problem in computational learning theory for researchers studying query-based learning of Boolean formulas, but it is incremental as it builds on existing query models.
The authors tackled the problem of learning definite Horn formulas by introducing closure queries as a new query type, and presented a polynomial-time algorithm using closure and equivalence queries that relates to the canonical Guigues-Duquenne basis.
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the so-called correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues-Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing full-fledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.