Advertisement

Integrating Lists, Multisets, and Sets in a Logic Programming Framework

Chapter
Part of the Applied Logic Series book series (APLS, volume 3)

Abstract

The first order theories of lists, bags, compact-lists (i.e., lists where the number of contiguous occurrences of each element is immaterial), and sets are introduced via axioms. Such axiomatizations are shown to be especially suitable for the integration with free functor symbols governed by the classical Clark’s axioms in the context of Constraint Logic Programming. Adaptations of the extensionality principle to the various theories taken into account is then exploited in the design of unification algorithms for the considered data structures. All the theories presented can be combined providing frameworks to deal with several of the proposed data structures simoultaneously. The unification algorithms proposed can be combined (merged) as well to produce engines for such combination theories.

Keywords

Logic Program Logic Programming Unification Algorithm Axiom Schema Extensionality Principle 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arenas-Sánchez, P., and Dovier, A. Minimal Set Unification. In Proc. Seventh InVl Symp. on Programming Language Implementation and Logic Programming (1995), M. Hermenegildo and S. D. Swierstra, Eds., vol. 982 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, pp. 397–414.Google Scholar
  2. Belle, D., and Parlamento, F. Undecidability of Weak Membership Theories. In Proceedings of the International Conference on Logic and Algebra (in memory of R. Magari) (1994).SienaGoogle Scholar
  3. Clark, K. L. Negation as Failure. In Logic and Databases, H. Gallaire and J. Minker, Eds. Plenum Press, 1978, pp. 293–321Google Scholar
  4. Dovier, A. Computable Set Theory and Logic Programming. PhD thesis, Università degli Studi di Pisa, 1996. In preparationGoogle Scholar
  5. Dovier, A., Omodeo, E. G., and Policriti, A. Hyperset constraint handling. Rr 21/94, Dipartimento di Matematica ed Informatica, Univ. di Udine, December 1994Google Scholar
  6. Dovier, A., Omodeo, E. G., Ponteiii, E., and Rossi., G. log: A Logic Programming Language with Finite Sets. In Proc. Eighth Int’l Conf. on Logic Programming (1991), K. Furukawa, Ed., The MIT Press, Cambridge, Mass., pp. 111–124Google Scholar
  7. Dovier, A., Omodeo, E. G., Pontelli, E., and Rossi, G. Embedding Finite Sets in a Logic Programming Language. In Selected papers from 3 rd Int’l Workshop on Extension of Logic Programming (1993), E. Lamma and P. Mello, Eds., vol. 660 of Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin, pp. 150–167CrossRefGoogle Scholar
  8. Dovier, A., Omodeo, E. G., Pontelli, E., and Rossi, G. log: A Language for Programming in Logic with Finite Sets. To appear in the Journal of Logic Programming, 1996Google Scholar
  9. Dovier, A., and Rossi, G. Embedding Extensional Finite Sets in CLP. In Proc. of Int’l Logic Programming Symposium, ILPS’93 (1993), D. Miller, Ed., The MIT Press, Cambridge, Mass., pp. 540–556Google Scholar
  10. Kapur, D., and Narendran, P. NP-completeness of the set unification and matching problems. In 8th International Conference on Automated Deduction (1986), J. H. Siekmann, Ed., vol. 230 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, pp. 489–495CrossRefGoogle Scholar
  11. Lassez, J. L., Mäher, M. J., and Marriot, K. Unification revisited. In Lecture Notes in Computer Science (1986), vol. 306Google Scholar
  12. Lloyd, J. W. Foundations of Logic Programming. Springer-Verlag, Berlin, 1987. Second editionCrossRefzbMATHGoogle Scholar
  13. Martelli, A., and Montanari, U. An efficient unification algorithm. ACM Transactions on Programming Languages and Systems 4 (1982), pp. 258–282CrossRefzbMATHGoogle Scholar
  14. Omodeo, E. G., Policriti, A., and Rossi., G. Che genere di insiemi/multi-insiemi/iperin- siemi incorporare nella programmazione logica? In D. Saccà, Ed., Proc. Eigth Italian Conference on Logic Programming (1993), pp. 55–70Google Scholar
  15. Parlamento, F., and Policriti, A. Decision Procedures for Elementary Sublanguages of Set Theory IX. Unsolvability of the Decision Problem for a Restricted Subclass of ¿o-Formulas in Set Theory. Communications of Pure and Applied Mathematics 41 (1988), pp. 221–251CrossRefzbMATHMathSciNetGoogle Scholar
  16. Paterson, M. S., and Wegman, M. N. Linear unification. Tech. rep., IBM Thomas J. Watson Research Center, Yorktown Heights, 1976Google Scholar
  17. Tarski, A., and Givant, S.A Formalization of Set Theory without Variables, vol. 41 of Colloquium Publications. American Mathematical Society, 1986Google Scholar
  18. Vaught, R. L. On a Theorem of Cobham Concerning Undecidable Theories. In Proceedings of the 1960 International Concress (1962), E. Nagel, P. Suppes, and A. Tarski, Eds., Stanford University Press, Stanford, pp. 14–25Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di PisaItalia
  2. 2.Dipartimento di Matematica e InformaticaUniversità di UdineItalia
  3. 3.Dipartimento di MatematicaUniversità di ParmaItalia

Personalised recommendations