Negation with logical variables in conditional rewriting

  • Chilukuri K. Mohan
  • Mandayam K. Srivas
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)


We give a general formalism for conditional rewriting, with systems containing conditional rules whose antecedents contain literals to be shown satisfiable and/or unsatisfiable. We explore semantic issues, addressing when the associated operational rewriting mechanism is sound and complete. We then give restrictions on the formalism which enable us to construct useful and meaningful specifications using the proposed operational mechanism.


Logic Program Logic Programming Function Symbol Logical Variable Ground Term 
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. [BBK]
    J.C.M. Baeten, J.A. Bergstra, J.W. Klop, Term Rewriting Systems with Priorities, Proc. 2nd RTA Conf., Bourdeaux, Springer-Verlag LNCS 256, pp83–94, 1987.Google Scholar
  2. [BDJ]
    D.Brand, J.A.Darringer, W.Joyner, Completeness of Conditional Reductions, IBM Res. Rep. RC7404, 1978.Google Scholar
  3. [BK]
    J.A. Bergstra, J.W. Klop, Conditional Rewrite Rules: Confluency and Termination, JCSS 32, pp.323–362, 1986.Google Scholar
  4. [Cl]
    K.L. Clark, Negation as Failure, in Logic and Databases, H. Gallaire & J. Minker (eds.), Plenum, NY, pp293–322, 1978.Google Scholar
  5. [CL]
    C.L. Chang, R.C. Lee, Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.Google Scholar
  6. [Co]
    H. Comon, Sufficient Completeness, Term Rewriting Systems, and “Anti-Unification”, Proc. 8th CADE, Springer-Verlag LNCS 230, pp128–140, 1986.Google Scholar
  7. [De]
    N. Dershowitz, Termination of Rewriting, Proc. First RTA Conf., Dijon, Springer-Verlag LNCS 202, pp180–224, 1985.Google Scholar
  8. [DL]
    D. DeGroot, G. Lindstrom, Logic Programming: Functions, Relations and Equations, Prentice Hall (NJ), 1986.Google Scholar
  9. [DP]
    N. Dershowitz, D.A. Plaisted, Logic Programming cum Applicative Programming, Proc. 1985 Symp. on Logic Programming, Boston, 1985.Google Scholar
  10. [Fa]
    M. Fay, First-Order Unification in an Equational Theory, Proc. 4th CADE, Austin (Texas), 1979, pp161–167.Google Scholar
  11. [Fi]
    M. Fitting, A Kripke-Kleene Semantics for Logic Programs, The Journal of Logic Programming, vol.4, Elsevier Science Pub., 1985, pp295–312.Google Scholar
  12. [Fr]
    L. Fribourg, Oriented Equational Clauses as a Programming Language, Proc. 11th ICALP, Antwerp (Belgium), July 1984.Google Scholar
  13. [GM]
    J.A. Goguen, J. Meseguer, Equality, Types, Modules and Generics for Logic Programming, J. of Logic Programming, Vol. 1, No.2, 1984, pp179–210.Google Scholar
  14. [HO]
    G. Huet, D.S. Oppen, Equations and Rewrite Rules: A Survey, Tech.Rep. CSL-111, SRI Int'l., California, 1980.Google Scholar
  15. [Hul]
    J.M. Hullot, Canonical Forms and Unification, Proc. 5th CADE, Springer-Verlag LNCS 87, April 1980.Google Scholar
  16. [Hus]
    H. Hussmann, Unification in Conditional-Equational Theories, Proc. EUROCAL Conf. at Linz (Austria), Springer-Verlag, LNCS 204, Apr. 1985, pp543–553.Google Scholar
  17. [JK]
    J.-P. Jouannaud, E. Kounalis, Proofs by Induction in Equational Theories without Constructors, Symp. on Logic in C.S., Cambridge (Mass.), USA, 1986, pp358–366.Google Scholar
  18. [JW]
    J.-P. Jouannaud, B. Waldmann, Reductive Conditional Term Rewriting Systems, Proc. Third TC2 Working Conf. on the Formal Description of Prog. Concepts, Ebberup, Denmark, Aug. 1986.Google Scholar
  19. [Ka1]
    S. Kaplan, Fair Conditional Term Rewriting Systems: Unification, Termination and Confluence, Res.Rep. 194, Universite de Paris-Sud, Orsay, Nov. 1984.Google Scholar
  20. [Ka2]
    S. Kaplan, Positive/Negative Conditional Rewriting, Proc. First Int'l. Workshop on Conditional Term Rewriting Systems, Orsay, Springer-Verlag LNCS 308, 1988, pp129–143.Google Scholar
  21. [KJ]
    S.Kaplan, J.-P.Jouannaud (eds.), Proc. First Int'l. Workshop on Conditional Term Rewriting Systems, Orsay, Springer-Verlag LNCS 308, 1988.Google Scholar
  22. [Kou]
    E. Kounalis, Completeness in Data Type Specifications, Res. Rep. 84-R-92, C.R.I.N., Nancy (France) 1984.Google Scholar
  23. [Kow]
    R.A. Kowalski, Predicate Logic as a Programming Language, Information Processing 74, North Holland, Apr. 1974, pp556–574.Google Scholar
  24. [La1]
    D.S.Lankford, Canonical Inference, Rep. ATP-32, Dept. of Math. & C.S., Univ. of Texas at Austin, Dec. 1975.Google Scholar
  25. [La2]
    D.S. Lankford, Some New Approaches to the Theory and Applications of Conditional Term Rewriting Systems, Research Report MTP-6, Univ. of Louisiana, Ruston, 1979.Google Scholar
  26. [Li]
    G. Lindstrom, Functional Programming and the Logical Variable, Proc. ACM POPL Symp., Jan. 1985.Google Scholar
  27. [Mo]
    C.K.Mohan, Negation in Equational Reasoning and Conditional Specifications, Ph.D. Thesis, State University of New York at Stony Brook, 1988.Google Scholar
  28. [Mo2]
    C.K.Mohan, Priority Rewriting: Semantics, Confluence and Conditionals, Proc. 3rd RTA Conf., Chapel Hill, 1989.Google Scholar
  29. [MS1]
    C.K. Mohan, M.K. Srivas, Function Definitions in Term Rewriting and Applicative Programming, Information and Control, Academic Press, New York, Vol.71, No.3, Dec. 1986, pp186–217.Google Scholar
  30. [MS2]
    C.K. Mohan, M.K. Srivas, Conditional Specifications with Inequational Assumptions, Proc. First Int'l. Workshop on Conditional Term Rewriting Systems, Orsay, Springer-Verlag LNCS 308, 1988, pp161–178.Google Scholar
  31. [MSK]
    C.K.Mohan, M.K.Srivas, D.Kapur, Inference Rules and Proof Procedures for Inequations, (to appear) Journal of Logic Programming, 1989.Google Scholar
  32. [Na]
    M.L. Navarro, Tecnicas de Reescritura para especificaciones condicionales, These Doctorale de l'Universite Polytechnique de Catalunya, Barcelona (Spain), 1987.Google Scholar
  33. [PEE]
    U. Pletat, G. Engels, H.D. Ehrich, Operational Semantics of Algebraic Specifications with Conditional Equations, 7eme C.A.A.P., Lille (France), 1982.Google Scholar
  34. [Red]
    U. Reddy, Narrowing as the Operational Semantics of Functional Languages, Proc. IEEE Logic Programming Symp., Boston, 1985.Google Scholar
  35. [Rei]
    R. Reiter, On Closed World Data Bases, in Logic and Data Bases, H. Gallaire & J. Minker (eds.), Plenum, NY, 1978.Google Scholar
  36. [Rem]
    J.-L. Remy, Etudes des systemes de reecriture conditionnels et application aux types abstraits algebriques, These d'Etat, Nancy (France), 1982.Google Scholar
  37. [Ret]
    P. Rety, Improving Basic Narrowing Techniques, Proc. 2nd RTA Conf., Bourdeaux, Springer-Verlag LNCS 256, pp228–241, 1987.Google Scholar
  38. [Sl]
    J.R. Slagle, Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity, J. ACM, Vol.21, No.4, 1974, pp622–642.Google Scholar
  39. [Th]
    J.J.Thiel, Stop Losing Sleep over Incomplete Specifications, Proc. 11th ACM POPL Symp., 1983.Google Scholar
  40. [ZR]
    H. Zhang, J.L. Remy, Contextual Rewriting, Proc. Conf. on Rewriting Techniques and Applications, Dijon (France), Springer-Verlag, LNCS 202, June 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Chilukuri K. Mohan
    • 1
  • Mandayam K. Srivas
    • 2
  1. 1.School of Computer & Info. Sci.Syracuse UniversitySyracuse
  2. 2.Odyssey Research Associates, Inc.Ithaca

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