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. The recent Metagol system efficiently solves MIL-problems by relying on the procedural bias imposed by Prolog. Its focus on positive examples, however, effects that Metagol can detect the derivability of negative examples only at a later check, which can severely hit performance. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP). Using a sophisticated ASP solver, we may expect that violations of negative examples can be propagated directly, but such an effect has never been explicitly exploited for general MIL. In fact, 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 by modeling the procedural bias. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to the relevant ones. Moreover, by abstracting from term manipulations in the encoding and exploiting the HEX interface mechanism, the import of such constants can be prevented completely in order to avoid the grounding bottleneck. An experimental evaluation shows promising results.

Derivation Reduction of Metarules in Meta-interpretive Learning

“…Many ILP systems, such as BLIP [7], Clint [29], DIALOGS [9], MOBAL [14], and MIL-HEX [13], use metarules 3 (or variants of them). Non-ILP program induction systems, such as ProPPR [32], SYNTH [1], and DILP [8], also use variants of metarules.…”

Inductive logic programming at 30

“…a program that reasons about programs. Meta-level approaches then often delegate the search for a hypothesis to an off-the-shelf solver (Corapi et al, 2011;Cropper & Muggleton, 2016;Law et al, 2014;Kaminski et al, 2018;Schüller & Benz, 2018;Evans et al, 2021;Cropper & Morel, 2021a) after which the meta-level solution is translated back to a standard solution for the ILP task. In other words, instead of writing a procedure to search in a top-down or bottom-up manner, most meta-level approaches formulate the learning problem as a declarative search problem.…”

“…The main advantage of meta-level approaches is that they can more easily learn recursive programs and optimal programs (Corapi et al, 2011;Law et al, 2014;Cropper & Muggleton, 2016;Kaminski et al, 2018;Evans et al, 2021;Cropper & Morel, 2021a), which we discuss in Sects. 3 and 6 respectively.…”

“…3 and 6 respectively. Moreover, whereas classical ILP systems were almost entirely based on Prolog, meta-level approaches use diverse techniques and technologies, such as ASP solvers (Corapi et al, 2011;Law et al, 2014;Kaminski et al, 2018;Cropper & Morel, 2021a;Evans et al, 2021), which we expand on in Sect. 7.…”

“…Most meta-level approaches encode the ILP learning task as a single static meta-level program (Corapi et al, 2011;Law et al, 2014;Kaminski et al, 2018;Evans et al, 2021).…”