Cited by 29Logic, Reasoning, and KnowledgeData Mining Algorithms and ApplicationsMachine Learning and Algorithms

Logical reduction of metarules

Open access
Cropper, Andrew, Tourret, Sophie·2020·Machine Learning

Abstract

Many 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.

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  • Compared to Metagol, Popper does not need metarules, so can learn programs with any arity predicates.

    “Compared to Metagol, Popper does not need metarules (Cropper and Tourret 2020), so can learn programs with any arity predicates.”

    From Learning programs by learning from failures (2021) · cites this paper as Cropper and Tourret 2020

    Section 2.1 says Metagol-style meta-interpretive learners use metarules, supporting the comparison’s Metagol side. The passages found do not discuss Popper, so they do not establish that Popper needs no metarules or can learn programs with predicates of any arity. Page numbers were not available in our copy. (LLM, conf=0.82)

    Experimental — accuracy not yet measured
  • A user must either provide a set of metarules, or use a set of metarules restricted to a certain fragment of logic, e.g. dyadic Datalog.

    “Ausermusteither(i)provideasetofmetarules, or (ii) use a set of metarules restricted to a certain fragment of logic, e.g. dyadic Datalog (Cropper and Tourret 2020).”

    From Learning programs by learning from failures (2021) · cites this paper as Cropper and Tourret 2020

    The Introduction says suitable metarules are commonly assumed to be supplied as background knowledge, and §3.1.1 studies syntactically restricted fragments. The paper also discusses chained dyadic Datalog, but these passages do not say a user must choose between supplying metarules and using a restricted fragment. (LLM, conf=0.83)

    Experimental — accuracy not yet measured
  • It is impossible to generate a finite and complete set of metarules for a singleton-free fragment of monadic and dyadic Datalog.

    “It is impossible to generate a finite and complete set of metarules for a singleton-free fragment of monadic and dyadic Datalog (Cropper and Tourret 2020).”

    From Learning programs by learning from failures (2021) · cites this paper as Cropper and Tourret 2020

    Section 5.3.1 (page unavailable) says the singleton-free fragment has no derivation reduction for arity at least two, supporting the claim if “complete” means derivationally complete. But the same summary says it has an entailment reduction to a finite set. The unqualified claim therefore overstates what is impossible. (LLM, conf=0.88)

    Experimental — accuracy not yet measured
  • The major problem with metarules is determining which one to use.

    “However, the major problem with metarules is determining whichonestouse(CropperandTourret2020).”

    From Learning programs by learning from failures (2021) · cites this paper as Cropper and Tourret 2020

  • Metarules are another popular syntactic bias used by many ILP approaches, including Metagol and, to an extent, ∂ ILP.

    “Metarules (Cropper and Tourret 2020) are another popular syntactic bias used by many ILP approaches (De Raedt and Bruynooghe 1992; Wang et al. 2014; Albarghouthi et al. 2017; Kaminski et al. 2018), including Metagol (Muggleton et al. 2015; Cropper et al. 2020; Cropper and Muggleton 2016) and, to an extent 5 , ∂ ILP (Evans and Grefenstette 2018).”

    From Learning programs by learning from failures (2021) · cites this paper as Cropper and Tourret 2020

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Research works printed but not linked: 2

  1. In J. Davis & J. Ramon (Eds.), Inductive logic programming-24th international conference, ILP 2014, Nancy, France, September 14-16, 2014. Revised selected papers, volume 9046 of Lecture Notes in Computer Science (pp. 62-75). Springer.
  2. Calimeri, F., Leone, N., & Manna, M. (Eds.), Logics in artificial intelligence-16th European conference, JELIA 2019, Rende, Italy, May 7-11, 2019, proceedings, volume 11468 of Lecture Notes in Computer Science (pp. 198-213). Springer.

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Authors
Cropper, A., & Tourret, S.
Affiliations
  • University of Oxford (GB)
  • Max Planck Society (DE)
Corresponding author
Cropper, Andrew
Venue
Machine Learning
Published
2019-11-20
Volume
109
Issue
7
Pages
1323-1369
ISSN
  • 0885-6125 (ISSN-L)
  • 1573-0565
OpenAlex
W2964129507
Cited by
29
References
67
Citations by year
2025: 2 · 2024: 2 · 2023: 6 · 2022: 4 · 2021: 7 · 2020: 7
FWCI
2.08
Type
journal article
Language
en
Open access
Locations
  • Machine Learning (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • HAL (submittedVersion, cc-by)
  • MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
University of Oxford
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
  • Physical Sciences › Computer Science › Information Systems › Data Mining Algorithms and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
Keywords
meta-rules, inductive logic programming, subsumption, logical consequence, SLD-resolution, hypothesis space

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