The Semantics of Nominal Logic Programs

  • James Cheney
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4079)

Abstract

Nominal logic programming is a form of logic programming with “concrete” names and binding, based on nominal logic, a theory of α-equivalence founded on swapping and freshness constraints. Previous papers have employed diverse characterizations of the semantics of nominal logic programs, including operational, denotational, and proof-theoretic characterizations; however, the formal properties and relationships among them have not been fully investigated. In this paper we give a uniform and improved presentation of these characterizations and prove appropriate soundness and completeness results. We also give some applications of these results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cheney, J., Urban, C.: Alpha-Prolog: A logic programming language with names, binding and a-equivalence. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 269–283. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Cheney, J.: The Complexity of Equivariant Unification. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 332–344. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Cheney, J.: A Simpler Proof Theory for Nominal Logic. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 379–394. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Cheney, J.: Completeness and Herbrand theorems for nominal logic. Journal of Symbolic Logic 81(1), 299–320 (2006)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Cheney, J.R.: Nominal Logic Programming. PhD thesis, Cornell University, Ithaca, NY (August 2004)Google Scholar
  6. 6.
    Darlington, J., Guo, Y.: Constraint logic programming in the sequent calculus. In: Pfenning, F. (ed.) LPAR 1994. LNCS, vol. 822, pp. 200–214. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (2002)MATHGoogle Scholar
  8. 8.
    Gabbay, M.J., Cheney, J.: A sequent calculus for nominal logic. In: Ganzinger, H. (ed.) Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004), Turku, Finland, pp. 139–148. IEEE, Los Alamitos (2004)CrossRefGoogle Scholar
  9. 9.
    Jaffar, J., Maher, M.J., Marriott, K., Stuckey, P.J.: The semantics of constraint logic programs. Journal of Logic Programming 37(1-3), 1–46 (1998)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Leach, J., Nieva, S., Rodríguez-Artalejo, M.: Constraint logic programming with hereditary Harrop formulas. Theory and Practice of Logic Programming 1(4), 409–445 (2001)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)MATHGoogle Scholar
  12. 12.
    Michaylov, S., Pfenning, F.: Higher-order logic programming as constraint logic programming. In: Position Papers for the First Workshop on Principles and Practice of Constraint Programming, Newport, Rhode Island, pp. 221–229 (April 1993)Google Scholar
  13. 13.
    Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. J. Logic and Computation 1(4), 497–536 (1991)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51, 125–157 (1991)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Pitts, A.M.: Nominal logic, a first order theory of names and binding. Information and Computation 183, 165–193 (2003)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. Theoretical Computer Science 323(1-3), 473–497 (2004)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Urban, C., Cheney, J.: Avoiding equivariant unification. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • James Cheney
    • 1
  1. 1.University of Edinburgh 

Personalised recommendations