Pac-Learning Recursive Logic Programs: Efficient Algorithms

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.Comment: See http://www.jair.org/ for any accompanying file

Louise: A Meta-Interpretive Learner for Efficient Multi-clause Learning of Large Programs

We present Louise, a new Meta-Interpretive Learner that performs efficient multi-clause learning, implemented in Prolog. Louise is efficient enough to learn programs that are too large to be learned with the current state-of-the-art MIL system, Metagol. Louise learns by first constructing the most general program in the hypothesis space of a MIL problem and then reducing this "Top program" by Plotkin's program reduction algorithm. In this extended abstract we describe Louise's learning approach and experimentally demonstrate that Louise can learn programs that are too large to be learned by our implementation of Metagol, Thelma

Subsumption Algorithms for Three-Valued Geometric Resolution

In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains only atoms with variables, equality, and existential quantifiers. The interpretation contains only atoms with constants. Because the atoms have no term structure, matching for geometric resolution is hard. We translate the matching problem into a generalized constraint satisfaction problem, and discuss several approaches for solving it efficiently, one direct algorithm and two translations to propositional SAT. After that, we study filtering techniques based on local consistency checking. Such filtering techniques can a priori refute a large percentage of generalized constraint satisfaction problems. Finally, we adapt the matching algorithms in such a way that they find solutions that use a minimal subset of the interpretation. The adaptation can be combined with every matching algorithm. The techniques presented in this paper may have applications in constraint solving independent of geometric resolution.Comment: This version was revised on 18.05.201