Deductive Synthesis of Recursive Plans in Linear Logic

  • Stephen Cresswell
  • Alan Smaill
  • Julian Richardson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1809)

Abstract

Linear logic has previously been shown to be suitable for describing and deductively solving planning problems involving conjunction and disjunction. We introduce a recursively defined datatype and a corresponding induction rule, thereby allowing recursive plans to be synthesised. In order to make explicit the relationship between proofs and plans, we enhance the linear logic deduction rules to handle plans as a form of proof term.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramsky, S.: Computational interpretations of linear logic. Theoretical Computer Science 111, 3–57 (1993) (Revised version of Imperial College Technical Report DoC 90/20)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bibel, W.: A deductive solution for plan generation. New Generation Computing 4, 115–132 (1986)MATHCrossRefGoogle Scholar
  3. 3.
    Brüning, S., Hölldobler, S., Schneeberger, J., Sigmund, U., Thielscher, M.: Disjunction in resource-oriented deductive planning. In: Proceedings of the International Symposium on Logic Programming, p. 670 (1993)Google Scholar
  4. 4.
    Bundy, A., Stevens, A., van Harmelen, F., Ireland, A., Smaill, A.: Rippling: A heuristic for guiding inductive proofs. Artificial Intelligence 62, 185–253 (1993); Also available from Edinburgh as DAI Research Paper No. 567MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Fikes, R.E., Nilsson, N.J.: STRIPS: A new approach to the application of theorem proving to problem solving. Artificial Intelligence 2, 189–208 (1971)MATHCrossRefGoogle Scholar
  6. 6.
    Ghassem-Sani, G.R., Steel, S.W.D.: Recursive plans. In: Hertzberg, J. (ed.) EWSP 1991. LNCS, vol. 522, pp. 53–63. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  7. 7.
    Girard, J.-Y.: Linear logic: its syntax and semantics. In: Girard, J.-Y., Lafont, Y., Regnier, L. (eds.) Advances in Linear Logic. London Mathematical Society Lecture Notes Series, vol. 222, Cambridge University Press, Cambridge (1995)CrossRefGoogle Scholar
  8. 8.
    Große, G., Hölldobler, S., Schneeberger, J.: Linear deductive planning. Journal of Logic and Computation 6(2), 233–262 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hesketh, J., Bundy, A., Smaill, A.: Using middle-out reasoning to control the synthesis of tail-recursive programs. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 310–324. Springer, Heidelberg (1992)Google Scholar
  10. 10.
    Hodas, J.S., Miller, D.: Logic programming in a fragment of intuitionistic linear logic. Information and Computation 110(2), 327–365 (1994); Extended abstract in the Proceedings of the Sixth Annual Symposium on Logic in Computer Science, Amsterdam, July 15-18 (1991)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ireland, A., Bundy, A.: Extensions to a Generalization Critic for Inductive Proof. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 47–61. Springer, Heidelberg (1996)Google Scholar
  12. 12.
    Jacopin, E.: Classical AI planning as theorem proving: The case of a fragment of linear logic. In: AAAI Fall Symposium on Automated Deduction in Nonstandard Logics, Technical Report FS-93-01, pp. 62-66. AAAI Press Publications, Palo Alto (1993)Google Scholar
  13. 13.
    Manna, Z., Waldinger, R.: How to clear a block: a theory of plans. Journal of Automated Reasoning 3(4), 343–377 (1986)MathSciNetGoogle Scholar
  14. 14.
    Masseron, M.: Generating plans in linear logic II: A geometry of conjunctive actions. Theoretical Computer Science 113, 371–375 (1993)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Masseron, M., Tollu, C., Vauzeilles, J.: Generating plans in linear logic I: Actions and proofs. Theoretical Computer Science 113(2), 349–371 (1993)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Nordström, B., Petersson, K., Smith, J.: Programming in Martin-Löf Type Theory. Oxford University Press, Oxford (1990)MATHGoogle Scholar
  17. 17.
    Stephan, W., Biundo, S.: Deduction based refinement planning. In: Drabble, B. (ed.) Proceedings of the 3rd International Conference on Artificial Intelligence Planning Systems (AIPS 1996), pp. 213–220. AAAI Press, Menlo Park (1996)Google Scholar
  18. 18.
    Sterling, L., Shapiro, E.: The Art of Prolog, 2nd edn. MIT Press, Cambridge (1994)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Stephen Cresswell
    • 1
  • Alan Smaill
    • 1
  • Julian Richardson
    • 1
  1. 1.Division of InformaticsUniversity of EdinburghEdinburghU.K.

Personalised recommendations