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Lemma Generalization and Non-unit Lemma Matching for Model Elimination

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Advances in Computing Science — ASIAN’99 (ASIAN 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1742))

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Abstract

In this paper, we study two lemma methods for accelerating Loveland’s model elimination calculus: One is lemma generalization and another is non-unit lemma matching. The derivation of lemmas in this paper is a dynamic one, i.e., lemma generation is repeatedly performed during an entire refutation search process. A derived lemma is immediately generalized by investigating the obtained subproof of the lemma. The lemma generalization increases the possibility of successful applications of the lemma matching rule. The non-unit lemma matching is an extension of the previously proposed unit lemma matching, and has the ability for stably speeding up model elimination calculus by monotonically reducing the refutation search space. We have implemented a PTTP-based theorem prover, named I-THOP, which performs unit lemma generalization and 2-literal non-unit lemma matching. We report good experimental results obtained with I-THOP.

This research was supported partly by Telecommunications Advancement Organization of Japan (TAO), and also partly by Grant-in-Aid from The Ministry of Education, Science and Culture of Japan.

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Authors and Affiliations

  1. Department of Computer Science and Media Engineering, Yamanashi University, Kofu, Yamanashi, 400-8511, Japan

    Koji Iwanuma & Kenichi Kishino

Authors
  1. Koji Iwanuma
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  2. Kenichi Kishino
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Editors and Affiliations

  1. Chennai Mathematical Institute, 92 G.N. Chetty Road, T. Nagar, Chennai, 600 017, India

    P. S. Thiagarajan

  2. School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore, 119260

    Roland Yap

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© 1999 Springer-Verlag Berlin Heidelberg

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Iwanuma, K., Kishino, K. (1999). Lemma Generalization and Non-unit Lemma Matching for Model Elimination. In: Thiagarajan, P.S., Yap, R. (eds) Advances in Computing Science — ASIAN’99. ASIAN 1999. Lecture Notes in Computer Science, vol 1742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46674-6_15

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  • DOI: https://doi.org/10.1007/3-540-46674-6_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66856-5

  • Online ISBN: 978-3-540-46674-1

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