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Non-situation Calculus and Database Systems

  • Pedro A. Matos
  • João P. Martins
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1762)

Abstract

Non-situation calculus is a way to describe dynamic worlds using first order logic, where a theory is written from the viewpoint of a situation (the propositional fluents hold in that situation). We introduced some functions to allow describing propositional fluents that hold in other situations. We define “progression” as a transformation that changes the situation represented by a non-situation calculus. The semantics counterpart of progression, function δ, transforms an interpretation of a non-situation calculus relative to a situation into an interpretation of a non-situation calculus relative to another situation.

We propose using non-situation calculus to study database dynamics by representing a database as a non-situation calculus theory, by representing transactions as changes and by associating the database that results from executing a transaction to the progression of the theory.

Keywords

Free Variable Order Theory Predicate Symbol Unary Predicate Situation Calculus 
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.

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References

  1. 1.
    Gerhard Brewka and Joachim Hertzberg. How to Do Things with Worlds: on Formalizing Actions and Plans. Journal of Logic and Computation, 3(5): 517–532, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Herbert B. Enderton. A mathematical introduction to logic. Academic Press Inc., 1972.Google Scholar
  3. 3.
    Richard E. Fikes and Nils J. Nilsson. STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving. Artificial Intelligence, 2:189–208, 1971.zbMATHCrossRefGoogle Scholar
  4. 4.
    Michael Gelfond and Vladimir Lifschitz. Representing action and change by logic programs. Journal of Logic Programming, 17:301–321, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Mathew L. Ginsberg and David E. Smith. Reasoning about Action I: A Possible Worlds Approach. Artificial Intelligence, 35:165–195, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Fausto Giunchiglia and Chiara Ghidini. Local model semantics, or contextual reasoning = locality and compatibility”. In Principles of Knowledge Representation and Reasoning: Proceedings of the Sixth International Conference, pages 282–289, 1998.Google Scholar
  7. 7.
    Fangzhen Lin and Ray Reiter. How to progress a database. Artificial Intelligence, 92:131–167, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Pedro A. Matos. Some properties of non-situation calculus. Technical report, Grupo de Inteligência Artificial, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa, Portugal, 1999. Available as http://www.gia.ist.utl.pt/~pedro/techrep/nsc.ps.Google Scholar
  9. 9.
    John McCarthy. First order theories of individual concepts and propositions. In Machine Intelligence, volume 9, pages 129–148. Ellis Horwood, 1979. Available as http://www-formal.stanford.edu/jmc/concepts.html.MathSciNetGoogle Scholar
  10. 10.
    John McCarthy and P. Hayes. Some philosophical problems from the standpoint of artificial intelligence. In Machine Intelligence, volume 4, pages 463–502. Edinburg University Press, 1969.zbMATHGoogle Scholar
  11. 11.
    Edwin P. D. Pednault. ADL and the State-Transition Model of Action. Journal of Logic and Computation, 4(5):465–512, 1994.Google Scholar
  12. 12.
    Raymond Reiter. On formalizing database updates: Preliminary report. In Proc. 3rd International Conference on Extending Database Technologies, pages 10–20, 1992.Google Scholar
  13. 13.
    Raymond Reiter. Proving properties of states in the situation calculus. Artificial Intelligence, 64:337–351, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Raymond Reiter. The projection problem in the situation calculus: A soundness and completeness result, with an application to database updates. In Proceedings of the International Conference on Knowledge Representation and Reasoning, 1996.Google Scholar
  15. 15.
    Stanley J. Rosenschein. Plan synthesis: A logical perspective. In Proceedings of the. Seventh International Joint Conference on Artificial Intelligence, pages 331–337, 1981.Google Scholar
  16. 16.
    Erik Sandewall and Yoav Shoham. Non-monotonic Temporal Reasoning. In Dov Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbok of Artificial Intelligence and Logic Programming, volume 4, pages 439–498. Oxford University Press, 1994.Google Scholar
  17. 17.
    Murray Shanahan. Solving the Frame Problem — A Mathematical Investigation of the Common Sense Law of Inertia. The MIT Press, 1997.Google Scholar
  18. 18.
    Marianne Winslett. Reasoning about action using a possible models approach. In Proceedings of the Seventh National Conference on Artificial Intelligence, pages 89–93, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Pedro A. Matos
    • 1
  • João P. Martins
    • 1
  1. 1.Instituto Superior TécnicoTechnical University of LisbonLisbon

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