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Extracting Information from Logical Proofs

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Logical Theory and Semantic Analysis

Part of the book series: Synthese Library ((SYLI,volume 63))

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Abstract

Logicians have long realized that the language of first order logic has great expressive power. In the early days of computers they tried to program the art of theorem-proving in the hope that the machine would then provide a steady stream of new and interesting results. Even although these hopes have faded more and more people are writing theorem proving programs. Why? Because the computer can extract information from the proofs of even simple theorems, that it can use for some other purpose. The techniques for doing this have been developed for theorem-provers that use local methods like resolution. Here we shall describe a technique for extraction of information from global theorem-provers of the kind developed by Prawitz, Kanger and others.

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Bibliography

  1. R. S. Boyer and J. S. Moore, ‘The Sharing of Structure in Theorem Proving Programs’, Machine Intelligence, Edinburgh Univ. Press, 7 (1972), pp. 101–116.

    Google Scholar 

  2. C. L. Chang and R. C. T. Lee, ‘Symbolic Logic and Mechanical Theorem Proving’, Academic Press, 1973.

    Google Scholar 

  3. J. L. Darlington, ‘Deductive Plan Formulation in Higher Order Logic’, Machine Intelligence, Edinburgh Univ. Press 7 (1972), pp. 129–137.

    Google Scholar 

  4. R. E. Fikes, ‘REF-ARF, A System for Solving Problems Stated as Procedures’, Artificial Intelligence, North-Holland Publ. Co. Amsterdam 1, pp. 27–120.

    Google Scholar 

  5. R. E. Fikes and N. J. Nilsson, ‘STRIPS, A New Approach to the Application of Theorem Proving to Problem Solving’, Artificial Intelligence, North-Holland Publ. Co. Amsterdam 2 (1971), pp. 189–208.

    Article  Google Scholar 

  6. R. W. Floyd, Toward Interactive Design of Correct Programs, Proc. IFIP Congress (1971) N. Holland Publ. Co., Amsterdam, pp. 1–4.

    Google Scholar 

  7. C. Cordell Green, ‘Theorem Proving by Resolution as a Basis for Question Answering Systems’, Machine Intelligence, Edinburgh Univ. Press 4 (1969), pp. 183–208.

    Google Scholar 

  8. P. J. Hayes, ‘Robotologic’, Machine Intelligence, Edinburgh Univ. Press 5 (1970), pp. 533–554.

    Google Scholar 

  9. P. J. Hayes, ‘A Logic of Actions’, Machine Intelligence, Edinburgh Univ. Press 6 (1971), pp. 495 - 520.

    Google Scholar 

  10. S. Kanger: A Simplified Proof Method for Elementary Logic, Computer Programming and Formal Systems (ed. by P. Braffort and D. Hirschberg ), N. Holland Publ. Co., Amsterdam, 1963.

    Google Scholar 

  11. T. A. Linden, A Summary of Programs Toward Proving Program Correctness, AFIPS Proc. Fall Joint Comp. Conf. (1972), N. Holland Publ. Co., Amsterdam, pp. 201–211.

    Google Scholar 

  12. D. Luckham and N. J. Nilsson, ‘Extracting Information from Resolution Proof Trees’, Artificial Intelligence, North-Holland Publ. Co. Amsterdam. 2 (1971), pp. 27–54.

    Article  Google Scholar 

  13. Z. Manna, S. Ness, and J. Vuillemin, ‘Fixpoint Approach to Theory of Computation’, Comm. Ass. Comp. Mach. 15 (1972), 528–536.

    Google Scholar 

  14. Z. Manna and R. J. Waldinger, ‘Towards Automatic Program Synthesis’, Comm. Ass. Comp. Mach. 14 (1971), 151–165.

    Google Scholar 

  15. B. H. Mayoh, Sprog, logik og tcenkende maskiner, Sprog og Virkelighed (ed. by M. Jacobsen ), Gyldendal, 1973.

    Google Scholar 

  16. J. McCarthy and P. J. Hayes, ‘Some Philosophical Problems from the Standpoint of Artificial Intelligence’, Machine Intelligence, Edinburgh Univ. Press 4 (1969), pp. 463–502.

    Google Scholar 

  17. N. J. Nilsson, Problem Solving Methods in Artificial Intelligence, McGraw-Hill, 1971.

    Google Scholar 

  18. D. Prawitz, ‘Advances and Problems in Mechanical Proof Procedures’, Machine Intelligence, Edinburgh Univ. Press 4 (1969), pp. 59–72.

    Google Scholar 

  19. 19]J. A. Robinson, ‘Computational Logic, the Unification Computation’, Machine Intelligence, Edinburgh Univ. Press 6 (1971), pp. 63–72.

    Google Scholar 

  20. E. Sandewall: ‘Representing Natural Language Information in Predicate Calculus’, Machine Intelligence, Edinburgh Univ. Press 6 (1971), 255–280.

    Google Scholar 

  21. E. Sandewall, ‘Formal Methods in the Design of Question-Answering Systems’, Artificial Intelligence, North-Holland Publ. Co. Amsterdam. 2 (1971), pp. 129–146.

    Article  Google Scholar 

  22. R. F. Simmons, ‘Natural Language Question-Answering Systems’, Comm. Ass. Comp. Mach. 13 (1970), 15–30.

    Google Scholar 

  23. A. M. Turing, ‘Computing Machinery and Intelligence’, Mind 59 (1950). reprinted in Mind and Machine (ed. by A. R. Anderson ), Prentice Hall, 1964.

    Google Scholar 

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© 1974 D. Reidel Publishing Company, Dordrecht-Holland

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Mayoh, B.H. (1974). Extracting Information from Logical Proofs. In: Stenlund, S., Henschen-Dahlquist, AM., Lindahl, L., Nordenfelt, L., Odelstad, J. (eds) Logical Theory and Semantic Analysis. Synthese Library, vol 63. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2191-3_6

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  • DOI: https://doi.org/10.1007/978-94-010-2191-3_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-2193-7

  • Online ISBN: 978-94-010-2191-3

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