Abstract
In this paper we motivate and present a new and improved transformation system for general E-unification. It can be seen as a modification of the original transformation system by Gallier and Snyder refined by ordinary unification and basic paramodulation. We present a short proof of completeness. Besides completeness we can also show an important property of the transformation system which is not known for the original system: independence of the selection rule. This motivates the abstraction of transformation sequences to equational proof trees thus obtaining static proof objects which facilitates finding further refinements of the procedure.
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References
L. Bachmair. Canonical Equational Proofs. Birkhäuser, Boston, 1991.
L. Bachmair, N. Dershowitz, and D. Plaisted. Completion Without Failure. In H. Ait-Kaci and M. Nivat, editors, Resolution of Equations in Algebraic Structures, Vol. 2, chapter 1, pages 1–30. Academic Press, Boston, 1989.
L. Bachmair, H. Ganzinger, Ch. Lynch, and W. Snyder. Basic Paramodulation and Superposition. In D. Kapur, editor, CADE'92, 11th International Conference on Automated Deduction, number 607 in LNCS, pages 462–476. Springer, 1992.
N. Dershowitz and J.-P. Jouannaud. Notations for Rewriting. In BECAT-1991, pages 162–172, Berlin, 1989. Springer.
N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In J.van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 245–321. Elsevier Science Publishers, Amsterdam, 1990.
D.J. Dougherty and P. Johann. An Improved General E-Unification Method. In M.E. Stickel, editor, CADE'90, 10th International Conference on Automated Deduction, number 449 in LNCS, pages 261–275, Berlin, 1990. Springer.
J. Gallier and W. Snyder. Complete Sets of Transformations for General E-Unification. Theoretical Computer Science, 67:203–260, 1989.
J. Hsiang and M. Rusinowitch. On Word Problems in Equational Theories. In 14th International Colloquium of Automata, Languages and Programming, number 267 in LNCS, pages 54–71, Berlin, 1987. Springer.
J.-M. Hullot. Canonical Forms and Unification. In CADE'80, 5th International Conference on Automated Deduction, number 87 in LNCS, pages 318–334, Berlin, 1980. Springer.
J.-P. Jouannaud and C. Kirchner. Solving Equations in Abstract Algebras: A Rule-Based Survey of Unification. In Computational Logic. Essays in honor of Alan Robinson, chapter 8, pages 257–321. MIT Press, 1991.
J.W. Lloyd. Foundations of Logic Programming. Springer, Berlin, 2 edition, 1987.
A. Martelli, C. Moiso, and C.F. Rossi. An Algorithm for Unification in Equational Theories. In International Symposium on Logic Programming, pages 180–186, 1986.
M. Moser. Complete Sets of Unifiers by Basic Superposition. Technical report, Technische Universität München, 1993.
R. Nieuwenhuis and A. Rubio. Basic Superposition is Complete. In B. Krieg-Brückner, editor, ESOP'92, 4th European Symposium on Programming, number 582 in LNCS, pages 371–389. Springer, 1992.
W. Nutt, P. Réty, and G. Smolka. Basic Narrowing Revisited. Journal of Symbolic Computation, 7:295–317, 1989.
W. Snyder. A Proof Theory for General Unification. Birkhäuser, Boston, 1991.
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Moser, M. (1993). Improving transformation systems for general E-unification. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_8
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DOI: https://doi.org/10.1007/978-3-662-21551-7_8
Publisher Name: Springer, Berlin, Heidelberg
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