Automatic Generation of Proof Search Strategies for Second-Order Logic

  • Raul H. C. Lopes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)


P2 is introduced: an algorithm for the automatic generation of proof search strategies from sets of examples of proofs. The proof search strategies are generated as sets of assertions (called methods) about the use of inference rules found in the examples. Sets of methods are prioritized and they can be compiled into clauses of a logic program. Proofs obtained for difficult problems in classical second-order logic are used as evidence of the adequacy of the methodology.


Modal Logic Inference Rule Free Variable Automatic Generation Sequent Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Peter B. Andrews, Dale A. Miller, Eve L. Cohen, and Frank Pfenning, Automating higher-order logic, In Bledsoe and Loveland [4], pp. 169–192.Google Scholar
  2. 2.
    Dana Angluin, William Gasarch, and Carl H. Smith, Training sequences, Theoretical Computer Science 66 (1989), 255–272.zbMATHMathSciNetGoogle Scholar
  3. 3.
    W.W. Bledsoe and Guohui Feng, Set-var, Journal of Automated Reasoning 11 (1993), 293–314.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    W.W. Bledsoe and D.W. Loveland (eds.), Automated theorem proving: After 25 years, American Mathematical Society, Providence-Rhode Island, 1984.Google Scholar
  5. 5.
    Alonzo Church, A formulation of the simple theory of types, Journal of Symbolic Logic 5 (1940), 56–68.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jaakko Hintikka, Truth definition, Skolem functions, and axiomatic set theory, The Bulletin of Symbolic Logic 4 (1998), no. 3, 303–337.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gérard P. Huet, A unification algorithm for typed λ-calculus,Theoretical Computer Science 1 (1975), 27–57.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Stephen Cole Kleene, Permutability of inferences in Gentzen’s calculi LK and LJ, Memoirs of the AMS, vol. 10, American Mathematical Society, 1952.Google Scholar
  9. 9.
    Raul H.C. Lopes, Inducing search methods from proofs, Tech. report, School of Computer Studies, University of Leeds, 1997.Google Scholar
  10. 10.
    Raul Henriques Cardoso Lopes, Inductive generalization of proof search strategies from examples, Ph.D. thesis, University of Leeds, 1998.Google Scholar
  11. 11.
    Dale A. Miller, iCompact representation of proofs, Studia Logica 4 (1987), 347–370.CrossRefGoogle Scholar
  12. 12.
    —, Unification under a mixed prefix, Journal of Symbolic Computation 14 (1992), 321–358.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Tom M. Mitchell, Generalization as search, Artificial Intelligence 18 (1982), 203–226.CrossRefMathSciNetGoogle Scholar
  14. 14.
    N. Shankar, Proof search in the intuitionistic sequent calculus, In Stickel [15], LNAI, 449, pp. 522–536.Google Scholar
  15. 15.
    M.E. Stickel (ed.), Proceedings of the 10th International Conference on Automated Deduction, Springer-Verlag, 1990, LNAI, 449.Google Scholar
  16. 16.
    Mark Tarver, An algorithm for inducing tactics from sequentzen proofs, Workshop on practical applications of automated reasoning, 1995, AISB.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Raul H. C. Lopes
    • 1
  1. 1.Departamento de Informática - UFESBrazil

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