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A goal oriented strategy based on completion

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Algebraic and Logic Programming (ALP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 632))

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Abstract

In this paper, a paramodulation calculus for equational reasoning is presented that combines the advantages of both Knuth-Bendix completion and goal directed strategies like the set of support strategy. Its soundness and completeness is proved, and finally the practical aspects of this method are discussed.

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References

  1. S. Anantharaman, J. Hsiang, and J. Mzali. SbReve2: A Term Rewriting Laboratory with (AC)Unfailing Completion. In: D. Plaisted (Ed.) Proc. of 3rd International Conference on Rewriting Techniques and Applications, Chapel Hill, N.C. (1989). Springer LNCS, 348–360.

    Google Scholar 

  2. L. Bachmair, N. Dershowitz and J. Hsiang. Orderings for Equational Proofs. Proc. of 1st Workshop on Logic in Computer Science (1986), 346–357.

    Google Scholar 

  3. L. Bachmair, N. Dershowitz, and D. Plaisted. Completion without Failure. Coll. On the Resolution of Equations in Algebraic Structures, Austin (1987), Academic Press.

    Google Scholar 

  4. M. P. Bonacina and J. Hsiang. On Fairness of Completion-Based Theorem Proving Strategies. In: R. V. Book (Ed.). Proc. of 4th Int. Conf. on Rewriting Techniques and Applications, Como (1991). Springer LNCS 488, 348–360.

    Google Scholar 

  5. C.L. Chang and R.C.T. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York 1973.

    Google Scholar 

  6. N. Dershowitz. Termination of Linear Rewriting Systems. In: S. Even, O. Kariv (Ed.). Proc. of 8th Int. Coll. on Automata, Languages and Programming, Acre, Israel (1981). Springer LNCS 115, 448–458.

    Google Scholar 

  7. N. Dershowitz, J.-P. Jouannaud. Notations for Rewriting. Bulletin of the EATCS, 43 (1991), 162–173.

    Google Scholar 

  8. D. J. Dougherty and P. Johann. An Improved General E-Unification Method. In: M. E. Stickel (Ed.). Proc. 10th Int. Conference on Automated Deduction, Kaiserslautern (1990). Springer LNCS 449, 261–275.

    Google Scholar 

  9. J. Hsiang and M. Rusinowitch. On Word Problems in Equational Theories. In: Th. Ottmann (Ed.). Proc. of 14th Int. Colloquium on Automata, Languages and Programming, Karlsruhe (1987). Springer LNCS 267, 54–71.

    Google Scholar 

  10. J. W. Klop. Term Rewriting Systems. In: S. Abramsky, D. M. Cabbay, and T. S. E. Maibaum (Eds.). Handbook of Logic in Computer Science, Oxford University Press, Oxford, to appear.

    Google Scholar 

  11. D.E. Knuth and P.B. Bendix. Simple Word Problems in Universal Algebra. In: J. Leech (Ed.). Computational Problems in Universal Algebra, Pergamon Press (1970).

    Google Scholar 

  12. E. Lusk and R. Overbeek. A short problem set for testing systems that include equational reasoning. Argonne National Laboratory 1984.

    Google Scholar 

  13. J. Morris. E-Resolution: Extensions of Resolution to Include the Equality Relation. In: Proc. of 1st Int. Joint Conf. on Artificial Intelligence, Washington, D.C. (1969), 287–294.

    Google Scholar 

  14. W. McCune. OTTER User's Manual, Argonne Report ANL-88-44 1988.

    Google Scholar 

  15. G. Robinson and L. Wos. Paramodulation and theorem-proving in firstorder theories with equality. In: B. Meltzer, & D. Michie, (Eds.): Machine Intelligence 4. Edinburgh, (1969), 135–150.

    Google Scholar 

  16. W. Snyder and Ch. Lynch. Goal Directed Strategies for Paramodulation. In: R. V. Book (Ed.). Proc. of 4th Int. Conf. on Rewriting Techniques and Applications, Como (1991). Springer LNCS 488, 150–161.

    Google Scholar 

  17. R. Socher-Ambrosius. A Goal Oriented Strategy Based on Completion. MPI-I-92-206, Max-Planck-Inst. f. Informatik, Saarbrücken 1992.

    Google Scholar 

  18. L. Wos, D. Carson, and G. Robinson. Efficiency and Completeness of the set of support strategy in theorem proving. Journal of the ACM 12, (1965), 698–709.

    Google Scholar 

  19. L. Wos. Automated Reasoning. 33 Basic Research Problems. Prentice-Hall, Englewood Cliffs 1988.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-W-6600, Saarbrücken, Germany

    Rolf Socher-Ambrosius

Authors
  1. Rolf Socher-Ambrosius
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Editor information

Hélène Kirchner Giorgio Levi

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© 1992 Springer-Verlag Berlin Heidelberg

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Socher-Ambrosius, R. (1992). A goal oriented strategy based on completion. In: Kirchner, H., Levi, G. (eds) Algebraic and Logic Programming. ALP 1992. Lecture Notes in Computer Science, vol 632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013842

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  • DOI: https://doi.org/10.1007/BFb0013842

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55873-6

  • Online ISBN: 978-3-540-47302-2

  • eBook Packages: Springer Book Archive

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