Pac-Learning Recursive Logic Programs: Efficient Algorithms

TL;DR

This paper introduces efficient algorithms for learning specific classes of recursive logic programs in polynomial time, establishing the boundaries of what is computationally feasible in this domain.

Contribution

It presents the first polynomial-time algorithms for learning certain recursive logic programs and defines the limits of efficient learnability for these classes.

Findings

Single k-ary recursive constant-depth determinate clauses are learnable.

Two-clause programs with a recursive and a non-recursive clause are learnable with a basecase oracle.

These classes are maximally general within polynomial-time learnability constraints.

Abstract

We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional ``basecase'' oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a computationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.