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Adding Constraints to Logic-based Formalisms

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Book cover The Logic Programming Paradigm

Part of the book series: Artificial Intelligence ((AI))

Summary

Constraints are predefined relations with a special implementation mechanism. Logic formalisms provide specific reasoning facilities. We look at the effect of adding constraints to existing logic-based executable formalisms, focusing on the semantics of the combined formalisms. We find that in cases where this has been successful the operations of the formalism can be formulated logically and then extended easily to constraints. In many cases a disjunctive property of the constraints is reflected in the combined formalism, to the detriment of efficiency.

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References

  1. K.R. Apt and R. N. Bol, Logic Programming and Negation: A Survey,Journal of Logic Programming, 19/20,, 9–71, 1994.

    Article  MathSciNet  Google Scholar 

  2. M. Baudinet, J. Chomicki and P. Wolper, Constraint-Generating Dependencies, in G. Gottlob and M.Y. Vardi (Eds.),Database Theory - ICDT’95,Lecture Notes in Computer Science 893, Springer-Verlag, 322–337, 1995.

    Google Scholar 

  3. F.S. de Boer and C. Palamidessi, From Concurrent Logic Programming to Concurrent Constraint Programming, in:Advances in Logic Programming Theory, Oxford University Press, 1994

    Google Scholar 

  4. H-J. Bürckert,A Resolution Principle for Constrained Logics,Artificial Intelligence 66, 235–271, 1994.

    Google Scholar 

  5. K.L. Clark, Negation as Failure, in H. Gallaire and J. Minker (Eds.),Logic and Databases, Plenum Press, New York, 293–322, 1978.

    Google Scholar 

  6. A. Colmerauer, Equations and Inequations on Finite and Infinite Trees,Proc. 2nd. Int. Conf. on Fifth Generation Computer Systems, Tokyo, 85–99, 1984.

    Google Scholar 

  7. J. Darlington, Y. Guo, H. Pull, A New Perspective on Integrating Functional and Logic Languages,Proc. Int. Conf. on Fifth Generation Computer Systems, 682–693, Ohmsha, Tokyo, 1992.

    Google Scholar 

  8. J. Dix, Stolzenburg, A Framework to Incorporate Non-Monotonic Reasoning into Constraint Logic Programming,Journal of Logic Programming 37, 47–76, 1998.

    MathSciNet  MATH  Google Scholar 

  9. M. Fitting, Modal Logic Should Say More Than It Does, in: J-L. Lassez, G. Plotkin (Eds.),Computational Logic: Essays in Honor of Alan Robinson, MIT Press, 113–135. 1991.

    Google Scholar 

  10. M. Fitting, Basic Modal Logic, in:Handbook of Mathematical Logic and Logic Programming,D. Gabbay(Ed.), Oxford University Press.

    Google Scholar 

  11. T. Frühwirth, Theory and Practice of Constraint Handling Rules,Journal of Logic Programming 37, 95–138, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. van Gelder, K. Ross, J.S. Schlipf, Unfounded Sets and Weil-Founded Semantics for General Logic Programs,Journal of the ACM, 38, 620–650, 1991.

    MATH  Google Scholar 

  13. M. Gelfond, V. Lifschitz, The Stable Model Semantics for Logic Programming,Proc. 5th International Conference on Logic Programming, 1070–1080, 1988.

    Google Scholar 

  14. P. van Hentenryck,Constraint Satisfaction in Logic Programming, MIT Press, 1989.

    Google Scholar 

  15. P. Van Hentenryck, V. Saraswat, Y. Deville, Design, Implementation and Evaluation of the Constraint Language cc(FD),Journal of Logic Programming 37, 139–164, 1998.

    Article  MATH  Google Scholar 

  16. J. Herbrand, Recherches sur la Théorie de la Démonstration, thesis, Université de Paris, 1930. In:Ecrits Logiques de Jacques Herbrand, PUF, Paris, 1968.

    Google Scholar 

  17. T. Hickey , Functional Constraints in CLP Languages, in:Constraint Logic Programming: Selected Research, F. Benhamou, A. Colmerauer (Eds.), MIT Press, 355–381, 1993.

    Google Scholar 

  18. ILOG, ILOG Solver 4.2 Reference Manual, 1998.

    Google Scholar 

  19. J. Jaffar, J-L. Lassez, Constraint Logic Programming,Proc. 14th ACM Symposium on Principles of Programming Languages, 111–119, 1987.

    Google Scholar 

  20. J. Jaffar, J-L. Lassez, J.W. Lloyd, Completeness of the Negation as Failure Rule,Proc. IJCAI–83, 500–506, 1983.

    Google Scholar 

  21. J. Jaffar, M.J. Maher, Constraint Logic Programming: A Survey,Journal of Logic Programming 19/20, 503–581, 1994.

    Article  MathSciNet  Google Scholar 

  22. J. Jaffar, M.J. Maher, K.G. Marriott, P.J. Stuckey, Semantics of Constraint Logic Programs,Journal of Logic Programming, 37, 1–46, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  23. A. C. Kakas, A. Michael, Integrating Abductive and Constraint Logic Programming,Proc. International Conference on Logic Programming, 399–413, MIT Press, 1995.

    Google Scholar 

  24. P. Kanellakis, G. Kuper, P. Revesz, Constraint Query Languages,Journal of Computer and System Sciences, 51(1), 26–52, 1995.

    Article  MathSciNet  Google Scholar 

  25. A.Klug, On Conjunctive Queries Containing Inequalities,Journal of the ACM 35, 1, 146–160, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  26. K. Kunen, Negation in Logic Programming,Journal of Logic Programming, 4, 289–308, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  27. G. Kuper, Aggregation in Constraint Databases,Proc. Workshop on Principles and Practice of Constraint Programming, 166–173, 1993.

    Google Scholar 

  28. J-L. Lassez, M. Maher, K.G. Marriott, Unification Revisited, in:Foundations of Deductive Databases and Logic Programming, J. Minker (Ed), Morgan Kaufmann, 587–625, 1988.

    Google Scholar 

  29. J-L. Lassez, K. McAloon, A Constraint Sequent Calculus,Proc. of 5th. Symp. on Logic in Computer Science, 52–62, 1990.

    Google Scholar 

  30. J-L. Lassez, K. McAloon, A Canonical Form for Generalized Linear Constraints,Journal of Symbolic Computation 13, 1–24, 1992.

    Google Scholar 

  31. B. Liu, J. Jaffar, Using Constraints to Model Disjunctions in Rule Based Programming,Proc. American National Conf. on Artificial Intelligence (AAAI), 1248–1255, 1996.

    Google Scholar 

  32. J.W. Lloyd,Foundations of Logic Programming, Springer-Verlag, Second Edition, 1987.

    MATH  Google Scholar 

  33. K. McAloon, C. Tretkoff, 2LP: A Logic Programming and Linear Programming System, Brooklyn College Computer Science Technical Report No 1989–21, 1989.

    Google Scholar 

  34. J.L. McCarthy, Circumscription - A Form of Non-Monotonic Reasoning,Artificial Intelligence, 13, 27–39, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  35. A. Mackworth, Consistency in Networks of Relations,Artificial Intelligence8(1), 99–118, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  36. M.J. Maher, Logic Semantics for a Class of Committed-Choice Programs,Proc. 4th International Conference on Logic Programming, 858–876, 1987.

    Google Scholar 

  37. M.J. Maher , Complete Axiomatizations of the Algebras of Finite, Rational and Infinite Trees,Proc. 3rd. Symp. Logic in Computer Science, 348–357, 1988. Full version: IBM Research Report, T.J. Watson Research Center.

    Google Scholar 

  38. M.J. Maher, A Logic Programming View of CLP,Proc. 10th International Conference on Logic Programming, 737–753, 1993.

    Google Scholar 

  39. M.J. Maher, Constrained Dependencies,Theoretical Computer Science 173, 113–149, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  40. M. Maher, D. Srivastava, Chasing Constrained Tuple-Generating Dependencies,Proc. ACM Symposium on Principles of Database Systems, 128–138, ACM Press, 1996.

    Google Scholar 

  41. A. Mal’cev , Axiomatizable Classes of Locally Free Algebras of Various Types, in:The Metamathematics of Algebraic Systems: Collected Papers, 1936–1967, Chapter 23, 262–281, 1971.

    Google Scholar 

  42. K. Marriott, P. Stuckey.Programming with Constraints: An Introduction, MIT Press, 1998.

    MATH  Google Scholar 

  43. L. Naish,Negation and Control in PROLOG, Lecture Notes in Computer Science 238, Springer-Verlag, 1986.

    Google Scholar 

  44. D. Nute , Defeasible Logic, in:Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3, D.M. Gabbay, C.J. Hogger, J.A. Robinson (Eds.), Oxford University Press, 1994, 353–395.

    Google Scholar 

  45. M. Odersky, M. Sulzmann, M. Wehr, Type Inference with Constrained Types,Theory and Practice of Object Systems, to appear.

    Google Scholar 

  46. J.-F. Puget, Constraint Programming,Proc. Joint Int. Conf. and Symp. on Logic Programming, 3, MIT Press, 1996.

    Google Scholar 

  47. R. Ramakrishnan, Magic Templates: A Spellbinding Approach to Logic Programs,Journal of Logic Programming, 11, 189–216, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  48. R. Reiter, A Logic for Default Reasoning,Artificial Intelligence13, 81–132, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  49. J. A. Robinson, A Machine-Oriented Logic Based on the Resolution Principle,Journal of the ACM 12(1), 23–41, 1965.

    Article  MATH  Google Scholar 

  50. E. Shapiro, The Family of Concurrent Logic Programming Languages,ACM Computing Surveys 21, 412–510, 1989.

    Article  Google Scholar 

  51. J. Siekmann, Unification Theory,Journal of Symbolic Computation, 7, 207–274, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  52. D. Srivastava, R. Ramakrishnan, Pushing Constraint Selections,Journal of Logic Programming, 16, 361–414, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  53. M. Stickel, Automated Deduction by Theory Resolution,Journal of Automated Reasoning1, 333–355, 1984.

    MathSciNet  Google Scholar 

  54. P. Stuckey, Negation and Constraint Logic Programming,Information and Computation, 118(1), 12–33, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  55. P.J. Stuckey, V. Tam, Models for using Stochastic Constraint Solvers in Constraint Logic Programming,Proc. Conf. on Programming Language Implementation and Logic Programming, LNCS 1140, 423–437, 1996.

    Google Scholar 

  56. E. Tsang,Foundations of Constraint Satisfaction, Academic Press, 1993.

    Google Scholar 

  57. K. Ueda, Guarded Horn Clauses,Proc. Japanese Logic Programming Conf., LNCS 221, 1985.

    Google Scholar 

  58. K. Ueda, Concurrent Logic/Constraint Programming: The Next 10 Years, this volume.

    Google Scholar 

  59. D.A. Wolfram, M.J. Maher, J.-L. Lassez, A Unified Treatment of Resolution Strategies for Logic Programs,Proc. Second Int. Conf. on Logic Programming, Uppsala, 263–276, 1984.

    Google Scholar 

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Author information

Authors and Affiliations

  1. 1School of Computing and Information Technology, Griffith University, Nathan 4111, Australia

    Michael J. Maher

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  1. Michael J. Maher
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Editor information

Editors and Affiliations

  1. Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098, Amsterdam, SJ, The Netherlands

    Krzysztof R. Apt

  2. Department of Computer Science, University of Kentucky, 773 Anderson Hall, 40506-0046, Lexington, KY, USA

    Victor W. Marek  & Mirek Truszczynski  & 

  3. Computer Science Department, University at Stony Brook, Stony Brook, 11794-4400, NY, USA

    David S. Warren

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© 1999 Springer-Verlag Berlin Heidelberg

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Maher, M.J. (1999). Adding Constraints to Logic-based Formalisms. In: Apt, K.R., Marek, V.W., Truszczynski, M., Warren, D.S. (eds) The Logic Programming Paradigm. Artificial Intelligence. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60085-2_13

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  • DOI: https://doi.org/10.1007/978-3-642-60085-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64249-4

  • Online ISBN: 978-3-642-60085-2

  • eBook Packages: Springer Book Archive

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