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The Situation and State Calculus versus Branching Temporal Logic

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Book cover Recent Trends in Algebraic Development Techniques

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1589))

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Abstract

The situation calculus (SC) is a formalism for reasoning about action. Within SC, the notion of state of a given situation is usually characterized by the set of fluents that hold in that situation. However, this concept is insufficient for system specification. To overcome this limitation, an extension of SC is proposed, the situation and state calculus (SSC), where the concept of state is primitive, just like actions, situations and fluents. SSC is then compared with a branching temporal logic (BTL). A representation of BTL in SSC is defined and shown to establish a sound and complete encoding.

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We would like to thank our colleagues in the ASPIRE project, and also to Alberto Zanardo, Cristina Sernadas and Javier Pinto their valuable comments and suggestions at some stages of this work. This work was partially supported by FCT, the PRAXIS XXI Projects 2/2.1/MAT/262/94 SitCalc, PCEX/P/MAT/46/96 ACL, 2/2.1/TIT/1658/95 LogComp, the ProbLog initiative of CMA, as well as the ESPRIT IV Working Groups 22704 ASPIRE and 23531 FIREworks.

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References

  1. J. P. Burgess. Logic and time. Journal of Symbolic Logic, 44:566–582, 1979.

    Article  MathSciNet  Google Scholar 

  2. H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1: Initial Semantics, volume 6 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, New York, N.Y., 1985.

    Google Scholar 

  3. J. Fiadeiro and A. Sernadas. Structuring theories on consequence. In D. Sannella and A. Tarlecki, editors, Proceedings of the 5th Workshop on Recent Trends in Data Type Specification, volume 332 of LNCS, pages 44–72, Berlin, 1988. Springer.

    Chapter  Google Scholar 

  4. M. Gelfond, V. Lifschitz, and A. Rabinov. What are the limitations of the situation calculus? In Robert Boyer, editor, Automated Reasoning: Essays in Honor of Woody Bledsoe, pages 167–179. Kluwer Academic, Dordrecht, 1991.

    Chapter  Google Scholar 

  5. J. Goguen and R. M. Burstall. Introducing institutions. In E. Clarke and D. Kozen, editors, Logics of Programs: Workshop, Carnegie Mellon University, June 1983, volume 164 of LNCS, pages 221–256. Springer-Verlag, New York, N.Y., 1984.

    Chapter  Google Scholar 

  6. V. Lifschitz and A. Rabinov. Miracles in formal theories of action. Articial Intelligence, 38:225–237, 1989.

    Article  MathSciNet  Google Scholar 

  7. Z. Manna and A. Pnueli. Completing the temporal picture. Theoretical Computer Science, 93:97–130, 1991.

    Article  Google Scholar 

  8. J. McCarthy and P. Hayes. Some philosophical problems from the standpoint of artificial intelligence. In B. Meltzer and D. Michie, editors, Machine Intelligence 4, pages 463–502. Edinburgh University Press, Scotland, 1969.

    MATH  Google Scholar 

  9. J. Meseguer. General logics. In H.-D. Ebbinghaus et al, editor, Proc. Logic Colloquium’ 87. North-Holland, 1989.

    Google Scholar 

  10. R. Miller and M. Shanahan. Narratives in the situation calculus. Journal of Logic and Computation — Special Issue on Actions and Processes, 4(5):513–530, 1994.

    Article  MathSciNet  Google Scholar 

  11. J. Pinto and R. Reiter. Reasoning about time in the situation calculus. Annals of Mathematics and Artificial Intelligence: Papers in Honour of Jack Minker, 14(2–4):251–268, 1995.

    Article  MathSciNet  Google Scholar 

  12. J. Ramos. The situation and state calculus. In A. Drewery, G.-J. Kruijff and R. Zuber, editors, Proceedings of the Second ESSLLI Student Session, 1997.

    Google Scholar 

  13. R. Reiter. The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In V. Lifschitz, editor, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 359–380. Academic Press, San Diego, CA, 1991.

    Chapter  Google Scholar 

  14. R. Reiter. Proving properties of states in the situation calculus. Articial Intelligence, 64:337–351, 1993.

    Article  MathSciNet  Google Scholar 

  15. A. Sernadas, C. Sernadas, and J. Costa. Object specification logic. Journal of Logic and Computation, 1:7–25, 1995.

    MathSciNet  MATH  Google Scholar 

  16. A. Sernadas, C. Sernadas, and J. Ramos. A temporal logic approach to object certification. Data and Knowledge Engineering, 19:267–294, 1996.

    Article  Google Scholar 

  17. C. Stirling. Modal and temporal logics. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science. Volume 2. Background: Computational Structures, pages 477–563. Oxford University Press, 1992.

    Google Scholar 

  18. J. van Benthem. Correspondence theory. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, Volume II: Extensions of Classical Logic, volume 165 of Synthese Library, chapter II.4, pages 167–247. D. Reidel Publ. Co., Dordrecht, 1984.

    Chapter  Google Scholar 

  19. A. Zanardo. Branching-time logic with quantification over branches: The point of view of modal logic. Journal of Symbolic Logic, 61(1):1–39, 1996.

    Article  MathSciNet  Google Scholar 

  20. A. Zanardo, B. Barcellan, and M. Reynolds. Non-denability of the class of complete bundled trees. The Logic Journal of IGPL. To appear.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, IST, Lisbon, Portugal

    Jaime Ramos & Amílcar Sernadas

Authors
  1. Jaime Ramos
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  2. Amílcar Sernadas
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Lisbon, Campo Grande 1700, Lisbon, Portugal

    José Luiz Fiadeiro

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© 1999 Springer-Verlag Berlin Heidelberg

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Ramos, J., Sernadas, A. (1999). The Situation and State Calculus versus Branching Temporal Logic. In: Fiadeiro, J.L. (eds) Recent Trends in Algebraic Development Techniques. Lecture Notes in Computer Science, vol 1589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48483-3_19

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  • DOI: https://doi.org/10.1007/3-540-48483-3_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66246-4

  • Online ISBN: 978-3-540-48483-7

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