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International Workshop on Logic, Language, Information, and Computation

WoLLIC 2011: Logic, Language, Information and Computation pp 161–175Cite as

Dynamic Epistemic Algebra with Post-conditions to Reason about Robot Navigation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6642))

Abstract

Dynamic epistemic algebra establishes Galois connections and quantales as a basis for reasoning about knowledge in multi-agent systems. To date, these algebraic-axiomatic methods have been restricted to a positive fragment of dynamic epistemic logic with communication events only. This paper proposes Boolean algebraic extensions which overcome these limitations by generalizing dynamic epistemic algebra to scenarios where events can change facts in form of post-conditions. As an application of the new algebraic treatment of post-conditions, we devise and solve a topological map-based robot navigation example for which current axiomatics are insufficient.

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References

  1. Abramsky, S., Vickers, S.: Quantales, observational logic and process semantics. Mathematical Structures in Computer Science 3(02), 161–227 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baltag, A., Coecke, B., Sadrzadeh, M.: Algebra and sequent calculus for epistemic actions. In: Proceedings of the 2nd International Workshop on Logic and Communication in Multi-Agent Systems. Electronic Notes in Theoretical Computer Science, vol. 126, pp. 27–52 (2005)

    Google Scholar 

  3. Baltag, A., Coecke, B., Sadrzadeh, M.: Epistemic actions as resources. Journal of Logic and Computation 17, 555–585 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Proceedings of TARK 1998, pp. 43–56. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  5. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  6. Bělohlávek, R.: Fuzzy galois connections. Math. Log. Q. 45, 497–504 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Philips, C., Precup, D., Panangaden, P., Sadrzadeh, M.: Reasoning about factual games using information updates. In: Proc. of 9th Conference on Logic and the Foundations of Game and Decision Theory (to appear)

    Google Scholar 

  8. Philips, C., Precup, D., Panangaden, P., Sadrzadeh, M.: An algebraic approach to dynamic epistemic logic. In: Proc. of 23rd International Workshop on Description Logics (2010)

    Google Scholar 

  9. Davey, B.A., Priestley, H.A.: Introduction to lattices and order, 2nd edn. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  10. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  11. Herzig, A., De Lima, T.: Epistemic actions and ontic actions: A unified logical framework. In: Sichman, J.S., Coelho, H., Rezende, S.O. (eds.) IBERAMIA 2006 and SBIA 2006. LNCS (LNAI), vol. 4140, pp. 409–418. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Höfner, P., Struth, G.: Automated reasoning in kleene algebra. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 279–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Horn, A.: Reasoning about learning in robot navigation via algebraic dynamic epistemic logic. Master’s thesis. University of Oxford (2010)

    Google Scholar 

  14. Kripke, S.A.: A semantical analysis of modal logic I: Normal modal propositional calculi. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9, 67–96 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kuipers, B., Byun, Y.-T.: A robot exploration and mapping strategy based on a semantic hierarchy of spatial representations. Journal of Robotics and Autonomous Systems 8, 47–63 (1991)

    Article  Google Scholar 

  16. Möller, B.: Knowledge and games in modal semirings. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS/AKA 2008. LNCS, vol. 4988, pp. 320–336. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  17. Panangaden, P., Sadrzadeh, M.: Learning in a changing world: an algebraic modal logical approach. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 128–141. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Phillips, C.: An algebraic approach to dynamic epistemic logic. Master’s thesis. McGill University (2009)

    Google Scholar 

  19. Rasiowa, H., Sikorski, R.: The mathematics of metamathematics. Państwowe Wydawn, Naukowe (1968)

    MATH  Google Scholar 

  20. Sadrzadeh, M.: Actions and Resources in Epistemic Logic. PhD thesis. Université du Québec à Montréal (2006)

    Google Scholar 

  21. van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Inf. Comput. 204(11), 1620–1662 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. van Ditmarsch, H.: The logic of pit. Synthese 149(2) (2006)

    Google Scholar 

  23. van Ditmarsch, H., Kooi, B.: Semantic results for ontic and epistemic change. In: Bonanno, G., van der Hoek, W., Wooldridge, M. (eds.) Logic and the Foundations of Game and Decision Theory, pp. 87–117. Amsterdam University Press, Amsterdam (2008)

    Google Scholar 

  24. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Heidelberg (2007)

    Book  MATH  Google Scholar 

  25. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic epistemic logic with assignment. In: Proc. of AAMAS 2005, pp. 141–148. ACM, New York (2005)

    Google Scholar 

  26. van Ditmarsch, H., van Eijck, J., Wu, W.: One hundred prisoners and a lightbulb — logic and computation. In: Lin, F., Sattler, U. (eds.). AAAI Press, Menlo Park (2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Oxford University Computing Laboratory, Oxford, UK

    Alexander Horn

Authors
  1. Alexander Horn
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Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Gubkina 8, 117966, Moscow, Russia

    Lev D. Beklemishev

  2. Centro de Informática, Universidade Federal de Pernambuco, Avenida Prof Luis Freire s/n, Cidade Universitária, 50740-540, Recife, PE, Brazil

    Ruy de Queiroz

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Horn, A. (2011). Dynamic Epistemic Algebra with Post-conditions to Reason about Robot Navigation. In: Beklemishev, L.D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2011. Lecture Notes in Computer Science(), vol 6642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20920-8_18

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  • DOI: https://doi.org/10.1007/978-3-642-20920-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20919-2

  • Online ISBN: 978-3-642-20920-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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