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A New Algorithm for Computing Least Generalization of a Set of Atoms

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11770))

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Abstract

This paper provides a new algorithm of computing a least generalization of a set of atoms. Our algorithm is based on the notion of anti-combination that is the inverse substitution of a combined substitution. In contrast to an anti-unification algorithm that computes a least generalization of two atoms, anti-combination can compute a least generalization of (more than two) atoms in parallel. We evaluate the proposed algorithm using randomly generated data and show that anti-combination outperforms the iterative application of an anti-unification algorithm in general.

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Notes

  1. 1.

    It is often written as \(\{\, x_1/t_1,...,x_n/t_n \,\}\) [3, 10, 13].

  2. 2.

    We use the same symbol \(\le \) over Atom, but the meaning is clear from the context. Note that the relation is often used reversely in the literature, e.g. \(\sigma \ge \theta \) if \(\sigma =\)\( \theta \lambda \) [4].

  3. 3.

    Combination is called parallel composition in [13].

  4. 4.

    Here we draw underlines to help distinguishing 3 terms in P.

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Acknowledgment

This research is funded by Vietnam National University – Ho Chi Minh city (VNU-HCM) under grant number C2019-26-01. We thank Mikio Yoshida for useful discussion on the subject of this paper.

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Authors and Affiliations

  1. University of Information Technology, Ho Chi Minh City, Vietnam

    Hien D. Nguyen

  2. Wakayama University, Wakayama, Japan

    Chiaki Sakama

  3. Vietnam National University, Ho Chi Minh City, Vietnam

    Hien D. Nguyen

Authors
  1. Hien D. Nguyen
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  2. Chiaki Sakama
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Corresponding author

Correspondence to Chiaki Sakama .

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Editors and Affiliations

  1. Department of Computer Science, University of York, Heslington, UK

    Dimitar Kazakov

  2. Department of Computer Science, University of York, Heslington, UK

    Can Erten

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Nguyen, H.D., Sakama, C. (2020). A New Algorithm for Computing Least Generalization of a Set of Atoms. In: Kazakov, D., Erten, C. (eds) Inductive Logic Programming. ILP 2019. Lecture Notes in Computer Science(), vol 11770. Springer, Cham. https://doi.org/10.1007/978-3-030-49210-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-49210-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-49209-0

  • Online ISBN: 978-3-030-49210-6

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