288 research outputs found

    Learning programs by learning from failures

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    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.Comment: Accepted for the machine learning journa

    Efficient instance and hypothesis space revision in Meta-Interpretive Learning

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    Inductive Logic Programming (ILP) is a form of Machine Learning. The goal of ILP is to induce hypotheses, as logic programs, that generalise training examples. ILP is characterised by a high expressivity, generalisation ability and interpretability. Meta-Interpretive Learning (MIL) is a state-of-the-art sub-field of ILP. However, current MIL approaches have limited efficiency: the sample and learning complexity respectively are polynomial and exponential in the number of clauses. My thesis is that improvements over the sample and learning complexity can be achieved in MIL through instance and hypothesis space revision. Specifically, we investigate 1) methods that revise the instance space, 2) methods that revise the hypothesis space and 3) methods that revise both the instance and the hypothesis spaces for achieving more efficient MIL. First, we introduce a method for building training sets with active learning in Bayesian MIL. Instances are selected maximising the entropy. We demonstrate this method can reduce the sample complexity and supports efficient learning of agent strategies. Second, we introduce a new method for revising the MIL hypothesis space with predicate invention. Our method generates predicates bottom-up from the background knowledge related to the training examples. We demonstrate this method is complete and can reduce the learning and sample complexity. Finally, we introduce a new MIL system called MIGO for learning optimal two-player game strategies. MIGO learns from playing: its training sets are built from the sequence of actions it chooses. Moreover, MIGO revises its hypothesis space with Dependent Learning: it first solves simpler tasks and can reuse any learned solution for solving more complex tasks. We demonstrate MIGO significantly outperforms both classical and deep reinforcement learning. The methods presented in this thesis open exciting perspectives for efficiently learning theories with MIL in a wide range of applications including robotics, modelling of agent strategies and game playing.Open Acces

    Logical Reduction of Metarules

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    International audienceMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperform subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times

    On the limits of the Davidsonian approach : the case of copula sentences

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    Since Donald Davidson’s seminal work “The Logical Form of Action Sentences” (1967) event arguments have become an integral component of virtually every semantic theory. Over the past years Davidson´s proposal has been continuously extended such that nowadays event(uality) arguments are generally associated not only with action verbs but with predicates of all sorts. The reasons for such an extension are seldom explicitly justified. Most problematical in this respect is the case of stative expressions. By taking a closer look at copula sentences the present study assesses the legitimacy of stretching the Davidsonian notion of events and discusses its consequences. A careful application of some standard eventuality diagnostics (perception reports, combination with locative modifiers and manner adverbials) as well as some new diagnostics (behavior of certain degree adverbials) reveals that copular expressions do not behave as expected under a Davidsonian perspective: they fail all eventuality tests, regardless of whether they represent stage-level or individual-level predicates. In this respect, copular expressions pattern with stative verbs like know, hate, and resemble, which in turn differ sharply from state verbs like stand, sit, and sleep. The latter pass all of the eventuality tests and therefore qualify as true “Davidsonian state” expressions. On the basis of these empirical observations and taking up ideas of Kim (1969, 1976) and Asher (1993, 2000), an alternative account of copular expressions (and stative verbs) is provided, according to which the copula introduces a referential argument for a temporally bound property exemplification (= “Kimian state”). Considerations on some logical properties, viz. closure conditions and the latent infinite regress of eventualities, suggest that supplementing Davidsonian eventualities with Kimian states may yield not only a more adequate analysis of copula sentences but also a better understanding of eventualities in general
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