Exploiting Answer Set Programming with External Sources for Meta-Interpretive Learning

Abstract

Meta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules, which is implemented by the Metagol system based on Prolog. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP), which may result in performance gains as a result of efficient conflict propagation. However, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX-formalism, which is an extension of ASP that allows us to outsource the background knowledge, and we restrict the search space to compensate for a procedural bias in ASP. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to relevant ones. Moreover, by abstracting from term manipulations in the encoding and by exploiting the HEX interface mechanism, the import of such constants can be entirely avoided in order to mitigate the grounding bottleneck. An experimental evaluation shows promising results.

Learning higher-order logic programs

“…Figure 12 also shows that both HEXMIL and HEXMIL ho do not scale well in the number of training examples, especially the learning times. Our results in Section 4.5 help explain the poor scalability of HEXMIL and HEXMIL ho because more training examples typically means more constant symbols which in turn means a larger search complexity for both HEXMIL and HEXMIL ho , although this issue can be mitigated using state abstraction [23].…”

“…Metagol ho supports the invention of conditions and functions to an arbitrary depth, which goes beyond anything in the literature. We also introduce HEXMIL ho , which likewise extends HEXMIL [23], an answer set programming (ASP) MIL implementation, to support learning higher-order programs. As far as we are aware, HEXMIL ho is the first ASP-based ILP system that has been demonstrated capable of learning higher-order programs.…”

“…MIL was originally based on a Prolog meta-interpreter, although the MIL problem has also been encoded as an ASP problem [23]. The key difference between a MIL learner and a standard Prolog meta-interpreter is that whereas a standard Prolog meta-interpreter attempts to prove a goal by repeatedly fetching first-order clauses whose heads unify with a given goal, a MIL learner additionally attempts to prove a goal by fetching higherorder existentially quantified formulas, called metarules, supplied as BK, whose heads unify with the goal.…”

“…HEXMIL is an answer set programming (ASP) encoding of MIL introduced by Kaminski et al [23]. Whereas Metagol searches for a proof (and thus a program) using a meta-interpreter and SLD-resolution, HEXMIL searches for a proof by encoding the MIL problem as an ASP problem.…”

“…ASP solvers typically work in two phases: (1) a grounding phase, where rules are grounded, and (2) a solving phase, where reasoning on (propositional) rules leads to answer sets [19]. A straightforward ASP encoding of the MIL problem is infeasible in many cases, for reasons such as the grounding bottleneck of ASP and the difficulty in manipulating complex structures such as lists [23]. To mitigate these difficulties HEXMIL uses the HEX formalism [13] which allows ASP programs to interface with external sources.…”