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Towards Systematic Analysis of Theorem Provers Search Spaces: First Steps

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Logic, Language, Information and Computation (WoLLIC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4576))

Abstract

Being able to automatically analyze the search spaces of automated theorem provers is of the greatest importance. A method is proposed to do that. It is inspired by inductive tasks (e.g. discovering in mathematics and natural sciences). The key idea is to replace implicit genetic descriptions of the consequences in search spaces (i.e. the problem specification) by structural ones (describing the form of such consequences). The approach profits from the expressive power of term schematization languages and from the capabilities offered by existing powerful symbolic computation systems (Mathematica,...). A running software based on these ideas show evidence of the adequacy of the approach.

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References

  1. Amaniss, A., Hermann, M., Lugiez, D.: Set operations for recurrent term schematizations. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 333–344. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  2. Bernstein, M., Sloane, N.J.A.: Some Canonical Sequences of Integers. Linear Algebra and its Applications 226/228(1–3), 57–72 (1995)

    Article  MathSciNet  Google Scholar 

  3. Bouhoula, A., Kounalis, E., Rusinowitch, M.: SPIKE, an automatic theorem prover. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, pp. 460–462. Springer, London, UK (1992)

    Chapter  Google Scholar 

  4. Caferra, R., Leitsch, A., Peltier, N.: Automated Model Building. Applied Logic Series, vol. 31. Kluwer Academic Publishers, Boston (2004)

    MATH  Google Scholar 

  5. Chen, H., Hsiang, J.: Logic programming with recurrence domains. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) Automata, Languages and Programming. LNCS, vol. 510, pp. 20–34. Springer, Heidelberg (1991)

    Google Scholar 

  6. Comon, H.: Disunification: A survey. In: Lassez, J.-L., Plotkin, G. (eds.) Computational Logic: Essays in Honor of Alan Robinson, pp. 322–359. MIT Press, Cambridge (1991)

    Google Scholar 

  7. Comon, H.: Inductionless induction. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, ch. 14, pp. 913–962. North-Holland (2001)

    Google Scholar 

  8. Comon, H.: On unification of terms with integer exponents. Mathematical System Theory 28, 67–88 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dreben, B., Goldfarb, W.D.: The Decision Problem, Solvable Classes of Quantificational Formulas. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  10. Hermann, M., Galbavý, R.: Unification of Infinite Sets of Terms schematized by Primal Grammars. Theoretical Computer Science 176(1–2), 111–158 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kleene, S.C.: Introduction to Metamathematics. North-Holland, Amsterdam (1952)

    MATH  Google Scholar 

  12. Peltier, N.: Increasing the capabilities of model building by constraint solving with terms with integer exponents. Journal of Symbolic Computation 24, 59–101 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Peltier, N.: A General Method for Using Terms Schematizations in Automated Deduction. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 578–593. Springer, Heidelberg (2001)

    Google Scholar 

  14. Plotkin, G.D.: A note on inductive generalization. Machine Intelligence 5, 153–163 (1970)

    MathSciNet  Google Scholar 

  15. Plotkin, G.D.: A Further Note on Inductive Generalization. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence 6, chapter 8, pp. 101–124. Edinburgh University Press, Edinburgh (1971)

    Google Scholar 

  16. Schulz, S.: The E Equational Theorem Prover, http://www4.informatik.tu-muenchen.de/~schulz/WORK/eprover.html

  17. Walsh, T.: A divergence critic for inductive proof. Journal of Artificial Intelligence Research 4, 209–235 (1996)

    MATH  MathSciNet  Google Scholar 

  18. Wos, L.: Automated Reasoning, 33 Basic Research Problems. Prentice-Hall, Englewood Cliffs (1988)

    Google Scholar 

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Author information

Authors and Affiliations

  1. INPT, Avenue Allal Al Fassi, Madinat Al Irfane, Rabat, Morocco

    Hicham Bensaid

  2. LIG INPG/CNRS, 46, avenue Félix Viallet, 38031 Grenoble Cedex, France

    Ricardo Caferra & Nicolas Peltier

Authors
  1. Hicham Bensaid
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  2. Ricardo Caferra
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  3. Nicolas Peltier
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Daniel Leivant Ruy de Queiroz

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© 2007 Springer Berlin Heidelberg

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Bensaid, H., Caferra, R., Peltier, N. (2007). Towards Systematic Analysis of Theorem Provers Search Spaces: First Steps. In: Leivant, D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2007. Lecture Notes in Computer Science, vol 4576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73445-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-73445-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73443-7

  • Online ISBN: 978-3-540-73445-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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