Learning programs by learning from failures

Abstract

We describe an inductive logic programming (ILP) approach called learning from failures. In this approach, an ILP system (the learner) decomposes the learning problem into three separate stages: generate, test, and constrain. In the generate stage, the learner generates a hypothesis (a logic program) that satisfies a set of hypothesis constraints (constraints on the syntactic form of hypotheses). In the test stage, the learner tests the hypothesis against training examples. A hypothesis fails when it does not entail all the positive examples or entails a negative example. If a hypothesis fails, then, in the constrain stage, the learner learns constraints from the failed hypothesis to prune the hypothesis space, i.e. to constrain subsequent hypothesis generation. For instance, if a hypothesis is too general (entails a negative example), the constraints prune generalisations of the hypothesis. If a hypothesis is too specific (does not entail all the positive examples), the constraints prune specialisations of the hypothesis. This loop repeats until either (i) the learner finds a hypothesis that entails all the positive and none of the negative examples, or (ii) there are no more hypotheses to test. We introduce Popper, an ILP system that implements this approach by combining answer set programming and Prolog. Popper supports infinite problem domains, reasoning about lists and numbers, learning textually minimal programs, and learning recursive programs. Our experimental results on three domains (toy game problems, robot strategies, and list transformations) show that (i) constraints drastically improve learning performance, and (ii) Popper can outperform existing ILP systems, both in terms of predictive accuracies and learning times.

Inductive logic programming at 30

“…These methods rely on notions of generality (typically using theta-subsumption (Plotkin, 1971)), where one program is more general or more specific than another. A third new search approach has recently emerged called meta-level ILP (Inoue et al, 2013;Muggleton et al, 2015;Inoue, 2016;Law et al, 2020b;Cropper & Morel, 2021a). We discuss these approaches in turn.…”

“…Expressivity Because of the expressivity of logic programs, ILP can learn complex relational theories, such as cellular automata (Inoue et al, 2014;Evans et al, 2021), event calculus theories (Katzouris et al, 2015(Katzouris et al, , 2016, Petri nets (Bain & Srinivasan, 2018), answer set programs (ASP) (Law et al, 2014), and general algorithms (Cropper & Morel, 2021a). Because of the symbolic nature of logic programs, ILP can reason about hypotheses, which allows it to learn optimal programs, such as minimal time-complexity programs (Cropper & Muggleton, 2019) and secure access control policies (Law et al, 2020a).…”

“…2 To aid the reader, we coarsely compare old and new ILP systems, where new represents systems from the past decade. We use FOIL (Quinlan, 1990), Progol (Muggleton, 1995), Aleph (Srinivasan, 2001), TILDE (Blockeel & De Raedt, 1998), and HYPER (Bratko, 1999) as representative old systems and ILASP (Law et al, 2014), Metagol (Cropper & Muggleton, 2016), ILP (Evans & Grefenstette, 2018), and Popper (Cropper & Morel, 2021a) as representative new systems. This comparison, shown in Table 1, is, of course, vastly oversimplified, and there are many exceptions.…”

Ready, Steady, Go AI: A practical tutorial on fundamentals of artificial intelligence and its applications in phenomics image analysis

“… 49 Consequently, methods such as logic-based ML make use of inductive logic programming 50 to integrate information and patterns extracted from data with human knowledge in order to make predictions. 51 , 52 …”

“…49 Consequently, methods such as logic-based ML make use of inductive logic programming 50 to integrate information and patterns extracted from data with human knowledge in order to make predictions. 51,52 Various ML algorithms have been developed and used in plant phenotyping, as reviewed by Singh et al 47 and van Dijk et al 53 While unsupervised, supervised, and semi-supervised learning can be useful depending on the goal to be achieved, in this tutorial, we focus on supervised learning, with an aim to provide researchers with ways to identify and classify healthy, diseased, and spider mite-damaged tomato leaf images. DL ANN has undergone significant improvements, mainly by increasing its number of layers.…”