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Reasoning Web. Explainable Artificial Intelligence pp 196–231Cite as

Logic-Based Learning of Answer Set Programs

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11810))

Abstract

Learning interpretable models from data is stated as one of the main challenges of AI. The goal of logic-based learning is to compute interpretable (logic) programs that explain labelled examples in the context of given background knowledge. This tutorial introduces recent advances of logic-based learning, specifically learning non-monotonic logic programs under the answer set semantics. We introduce several learning frameworks and algorithms, which allow for learning highly expressive programs, containing rules representing non-determinism, choice, exceptions, constraints and preferences. Throughout the tutorial, we put a strong emphasis on the expressive power of the learning systems and frameworks, explaining why some systems are incapable of learning particular classes of programs.

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Notes

  1. 1.

    As the notions had not been defined at the time, they did not call it cautious induction, but the definitions are the same.

  2. 2.

    The original definitions of brave and cautious induction did not consider atoms which should not be present in an answer set (negative examples). Publicly available algorithms that realise brave induction, on the other hand, do allow for negative examples. We therefore upgrade the definitions in this tutorial to allow negative examples. Note that a negative example \(\mathtt {e}\) can be easily simulated by adding a rule to the background knowledge and giving \(\mathtt {a}\) as a positive example (where \(\mathtt {a}\) is a new atom that does not appear anywhere in the original task).

  3. 3.

    This is a slight simplification. In the ASPAL algorithm, this is a choice rule using conditional literals, in order to delegate the grounding of the possible constants to the ASP solver. The ground version of ASPAL’s choice rule is identical to the one presented in this definition.

  4. 4.

    Both XHAIL [36] and ASPAL [7] support learning non-stratified programs, but the background knowledge and hypothesis space of each of the example tasks in [36] and [7] is stratified.

  5. 5.

    A graph is Hamiltonian if it contains a cycle that visits each node exactly once.

  6. 6.

    Details of the encodings can be found in [20,21,22].

  7. 7.

    In Algorithm 1.1 the set Relevant is a pair of sets of examples, the first set being relevant positive examples and the second set relevant negative examples. The notation on Line 5 means to add example re to the appropriate set, depending on whether it is a positive or a negative example.

  8. 8.

    Note that to avoid cumbersome notation, we denote this \(E_{LAS}\) rather than \(E_{ILP_{LAS}}\).

  9. 9.

    In Table 1 the following two notations are used. For programs P and Q the relation \(P\equiv ^{s}Q\) means that for any program R \(AS(P \cup R) = AS(Q \cup R)\) and for a program P \(\mathcal {E}_c(BP)\) is the set of conjunctions of literals in every answer set of P.

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Authors and Affiliations

  1. Department of Computing, Imperial College London, London, UK

    Mark Law, Alessandra Russo & Krysia Broda

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  1. Mark Law
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  2. Alessandra Russo
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  3. Krysia Broda
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Correspondence to Alessandra Russo .

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Editors and Affiliations

  1. Technische Universität Dresden, Dresden, Sachsen, Germany

    Markus Krötzsch

  2. Bosch Center for Artificial Intelligence, Renningen, Germany

    Daria Stepanova

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Law, M., Russo, A., Broda, K. (2019). Logic-Based Learning of Answer Set Programs. In: Krötzsch, M., Stepanova, D. (eds) Reasoning Web. Explainable Artificial Intelligence. Lecture Notes in Computer Science(), vol 11810. Springer, Cham. https://doi.org/10.1007/978-3-030-31423-1_6

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