Learning Weakly Acyclic Horn Programs

We consider a general class of \weakly acyclic Horn programs" where the literals implied by the examples and the target clauses form an acyclic dependency graph. A Horn clause is transparent if all the terms in all its derivations from the target program are contained in the clause itself. A Horn program is transparent if all its clauses are transparent. We show that any subclass of rst-order weakly acyclic, transparent, and unambiguous Horn programs with constant arity is exactly learnable from equivalence, membership, and derivation order queries, provided the class has a polynomial-time subsumption procedure and obeys some closure conditions. In particular, these conditions are shown to be satissed by determinate Horn programs. The training examples are also required to be transparent, unambiguous, and give rise to acyclic dependency graphs among the literals implied by their antecedents. Unambiguity roughly means that there is no step in the derivation of the training examples (or the target clauses) that can potentially be generalized in more than one way. Transparency and weak acyclicity respectively generalize range-restricted and acyclic Horn clauses analyzed in our previous work. As a result, many useful programs such as member, length and multiply, as well as recursive deenitions of predicates such as above in the blocks world planning can be learned by our program.