Skip to main content
SpringerLink
Log in

The logic of totally and partially ordered plans: a deductive database approach

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

The problem of finding effective logic-based formalizations for problems involving actions remains one of the main application challenges of non-monotonic knowledge representation. In this paper, we show that complex planning strategies find natural logic-based formulations and efficient implementations in the framework of deductive database languages. We begin by modeling classical STRIPS-like totally ordered plans by means of Datalog1 S programs, and show that these programs have a stable model semantics that is also amenable to efficient computation. We then show that the proposed approach is quite expressive and flexible, and can also model partially ordered plans, which are abstract plans whereby each plan stands for a whole class of totally ordered plans. This results in a reduction of the search space and a subsequent improvement in efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Abieteboul, R. Hull and V. Vianu, Foundations of Databases (Addison-Wesley, 1995).

  2. K.R. Apt and M. Bezem, Acyclic programs, in: Proceedings Seventh International Conference on Logic Programming, eds. D.H.D. Warren and P. Szeredi (MIT Press, 1990) pp. 617–633.

  3. K.A. Bowen, Meta-level programming and knowledge representation, New Generation Computing 3(3) (1985) 359–383.

    Google Scholar 

  4. K.A. Bowen and R.A. Kowalski, Amalgamating language and metalanguage in logic programming, in: Logic Programming, eds. K.L. Clark and S.A. Tarnlund (Academic Press, 1982) pp. 153–173.

  5. A. Brogi, V.S. Subrahmanian and C. Zaniolo, Modeling sequential and parallel plans, Technical Report, Submitted for publication (1996).

  6. A. Brogi and F. Turini, Metalogic for knowledge representation, in: Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, eds. J.A. Allen, R. Fikes and E. Sandewall (Morgan-Kaufmann, 1990) pp. 100–106.

  7. A. Brogi and C. Zaniolo, Converting linear and nonlinear plans into parallel execution plans, Technical Report, Department of Computer Science, UCLA (1995).

  8. J. Chomicki, Polynomial-time computable queries in temporal deductive databases, PODS'90 (1990).

  9. J. Chomicki, Temporal deductive databases, in: Temporal Databases: Theory, Design and Implementation, eds. A. Tansel, J. Clifford, S. Gadia, S. Jagodia, A. Segev and R. Snodgrass (Benjamin/Cummings, 1993) pp. 294–320.

  10. K.L. Clark, Negation as failure, in: Logic and Databases, eds. H. Gallaire and J. Minker (1978).

  11. L. Corciulo, F. Giannotti and D. Pedreschi, Datalog with non-deterministic choice compute ndbptime, in: Proc. International Conference on Deductive and Object-Oriented Databases, DOOD'93 (1993).

  12. K. Erol, D.S. Nau and V.S. Subrahmanian, Complexity, decidability and undecidability results for domain-independent planning, Artificial Intelligence (1995).

  13. K. Eshgi and R.A. Kowalski, Abduction compared with negation as failure, in: Proceedings Sixth International Conference on Logic Programming, eds. G. Levi and M. Martelli (MIT Press, 1989) pp. 234–254.

  14. C. Evans, Negation-as-failure as an approach to the Hanks and McDermott problem, in: Proceedings Second Int'l Symp. on Artificial Intelligence (1989).

  15. R. Fikes and N. Nilsson, STRIPS: A new approach to the application of theorem proving in problem solving, Artificial Intelligence 2(3,4) (1971) 189–208.

    Google Scholar 

  16. M. Gelfond and V. Lifschitz, The stable model semantics for logic programming, in: Logic Programming: Proceedings of the Fifth Int`l Conf. and Symposium, eds. R.A. Kowalski and K. Bowen (1988) pp. 1070–1080.

  17. M. Gelfond and V. Lifschitz, Representing action and change by logic programs, Journal of Logic Programming 17 (1993) 301–322.

    Google Scholar 

  18. S. Hanks and D. McDermott, Nonmonotonic logic and temporal projection, Artificial Intelligence 33 (1987) 379–412.

    Google Scholar 

  19. J.W. Lloyd, Foundations of Logic Programming (Springer-Verlag, 2nd edition, 1987).

  20. V. Marek and V.S. Subrahmanian, The relationship between stable, supported, default and auto-epistemic semantics for general logic programs, Theoretical Computer Science 103 (1992) 365–386.

    Google Scholar 

  21. V. W. Marek and M. Truszczynski, Nonmonotonic Logic (Springer-Verlag, 1995).

  22. D. McAllester and D. Rosenblitt, Systematic nonlinear planning, in: Proceedings of the Ninth National Conference on Artificial Intelligence (MIT Press, 1991) pp. 634–639.

  23. J. McCarthy, Applications of circumsription to formalising common sense reasoning, Artificial Intelligence 26 (1986) 89–116.

    Google Scholar 

  24. D. McDermott, A temporal logic for reasoning about processes and plans, Cognitive Science 6 (1982) 101–155.

    Google Scholar 

  25. J. Pinto and R. Reiter, Temporal reasoning in logic programming: A case for the situation calculus, in: Proc. 1993 Intl. Conf. on Logic Programming (MIT Press, 1993) pp. 203–221.

  26. T. Przymusinski, On the declarative and procedural semantics of stratified deductive databases, in: Foundations of Deductive Databases and Logic Programming, ed. J. Minker (Morgan-Kaufmann, 1988) pp. 193–216.

  27. D. Saccà and C. Zaniolo, Stable models and non-determinism in logic programs with negation, in: Proc. 9th ACM Symp. on Principles of Database Systems (1990).

  28. E. Sacerdoti, The nonlinear nature of plans, in: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI-75) (1975) pp. 206–214.

  29. V.S. Subrahmanian and C. Zaniolo, Relating stable models and AI planning domains, in: Proc. 12th International Conference on Logic Programming, ICLP'95 (1995).

  30. A. Tate, Generating project networks, in: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI-77) (1977) pp. 889–900.

  31. J. Vaghani, K. Ramamohanarao, D.B. Kemp, Z. Somogyi, P.J. Stuckey, T.S. Leask and J. Harland, The Aditi deductive database system, VLDB Journal 3 (1994) 245–288.

    Google Scholar 

  32. D.H.D. Warren, An abstract prolog instruction set, Technical Report, SRI International (1983).

  33. D.S. Weld, An introduction to least commitment planning, A.I. Magazine (1995).

  34. C. Zaniolo, A unified semantics for active and deductive databases, in: Proceedings of the 1st International Workshop on Rules in Database Systems (1933) pp. 271–287.

  35. C. Zaniolo, Transaction-conscious stable model semantics for active database rules, in: Proc. International Conference on Deductive Object-Oriented Databases, DOOD'95 (1995).

  36. C. Zaniolo, N. Arni and K. Ong, Negation and aggregates in recursive rules: the ldl++ approach, in: Proc. International Conference on Deductive and Object-Oriented Databases, DOOD'93 (1993).

Download references

Authors
  1. Antonio Brogi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V.S. Subrahmanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Carlo Zaniolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brogi, A., Subrahmanian, V. & Zaniolo, C. The logic of totally and partially ordered plans: a deductive database approach. Annals of Mathematics and Artificial Intelligence 19, 27–58 (1997). https://doi.org/10.1023/A:1018995303452

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018995303452

Keywords

Search

Navigation