Probably approximately correct learning of Horn envelopes from queries

TL;DR

This paper introduces a polynomial-time probably approximately correct algorithm for learning the Horn envelope of any domain using an oracle, improving upon previous exponential-query methods.

Contribution

It adapts a known polynomial-time algorithm for Horn formulas to develop an efficient PAC learning algorithm for Horn envelopes from queries.

Findings

The algorithm operates in polynomial time.

It achieves probably approximately correct learning.

It reduces the number of queries compared to exponential methods.

Abstract

We propose an algorithm for learning the Horn envelope of an arbitrary domain using an expert, or an oracle, capable of answering certain types of queries about this domain. Attribute exploration from formal concept analysis is a procedure that solves this problem, but the number of queries it may ask is exponential in the size of the resulting Horn formula in the worst case. We recall a well-known polynomial-time algorithm for learning Horn formulas with membership and equivalence queries and modify it to obtain a polynomial-time probably approximately correct algorithm for learning the Horn envelope of an arbitrary domain.