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Composing decision procedures: the approach and a case study

  • Mauro Di Manzo
  • Paolo Pecchiari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 992)

Abstract

In this paper we address the problem of strengthening the inferential capabilities of an interactive theorem prover with complex and reusable proof procedures. We focus on the construction of proof procedures built out of decision procedures for (decidable) quantifierfree theories. The idea is to build proof procedures in a structured way. A set of deciders provides the low-level reasoning capabilities, while the high-level (i.e. strategical) reasoning procedures are to be synthesized on top of it. The main goal of the paper is to show that this approach has many advantages and is of wide applicability. As a case study we consider the synthesis of a proof procedure for the existential fragment of first order logic built on top of a prepositional decider. This procedure is particularly well suited for describing our approach, since in it there is a neat separation between the prepositional and the first order reasoning components.

Keywords

interactive theorem proving decision procedures 

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References

  1. [AG93]
    A. Armando and E. Giunchiglia. Embedding Complex Decision Procedures inside an Interactive Theorem Prover. Annals of Mathematics and Artificial Intelligence, 8(3–4):475–502, 1993.Google Scholar
  2. [And81]
    P.B. Andrews. Theorem Proving via General Matings. Journal of the ACM, 28(2):193–214, 1981.Google Scholar
  3. [BB92]
    M. Büro and H. Kleine Büning. Report on a SAT competition. Technical Report Nr. 110, FB 17-Mathematik/Informatik Universität Paderborn, Nov. 1992.Google Scholar
  4. [Bib82]
    W. Bibel. Automated Theorem Proving. Vieweg, Braunschweig, 1982.Google Scholar
  5. [BM88]
    R.S. Boyer and J.S. More. Integrating decision procedures into heuristic theorem provers: A case study of linear arithmetic. Machine Intelligence, 11:83–124, 1988.Google Scholar
  6. [DG79]
    B. Dreben and W.D. Goldfarb. The Decision problem — Solvable classes of quantificational formulas. Addison-Wesley Publishing Company Inc., 1979.Google Scholar
  7. [DP60]
    M. Davis and H. Putnam. A computing procedure for quantification theory. Journal of the ACM, 7:201–215, 1960.Google Scholar
  8. [Gil60]
    P.C. Gilmore. A proof Method for Quantification Theory: its Justification and Realization. IBM Journal on Research and Development, 4:28–35, 1960.Google Scholar
  9. [Giu92]
    F. Giunchiglia. The Getfol Manual — Getfol version 1. Technical Report 9204-01, DIST — University of Geneva, Genoa, Italy, 1992.Google Scholar
  10. [Jer88]
    R.G. Jeroslow. Computation-Oriented Reduction of Predicate to Prepositional Logic. Decision Support System, 4:183–197, 1988.Google Scholar
  11. [Joy76]
    W.H. Joyner. Resolution strategies as decision procedures. Journal of the ACM, 23(3):398–417, 1976.Google Scholar
  12. [LP90]
    S.J. Lee and D.A. Plaisted. Eliminating Duplication with the Hyper-Linking Strategy. Technical Report TR90-032, The University of North Carolina — Dept. of Computer Science, Aug. 1990.Google Scholar
  13. [NO78]
    G. Nelson and D.C. Oppen. Simplification by Cooperating Decision Procedures. ACM Transactions on Programming Languages and Systems, 1(2), Oct. 1979.Google Scholar
  14. [Pra60]
    D. Prawitz. An improved proof procedure. Theoria, 26:102–139, 1960.Google Scholar
  15. [Sti85]
    M. Stickel. Automated Deduction by Theory Resolution. Journal of Automated Reasoning, 4:333–356, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Mauro Di Manzo
    • 1
  • Paolo Pecchiari
    • 1
  1. 1.Mechanized Reasoning Group DISTUniversity of GenovaGenevaItaly

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