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Synthese

, Volume 167, Issue 2, pp 391–408 | Cite as

Ockham’s razor and reasoning about information flow

  • Mehrnoosh Sadrzadeh
Article

Abstract

What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? How much can we weaken and still be able to reason about multi-agent scenarios in a tidy compositional way? This paper provides some answers.

Keywords

Algebraic modal logic Galois adjoints Reasoning about knowledge and update 

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References

  1. Baltag, A., & Moss, L. S. (2004). Logics for epistemic programs. Synthese, 139.Google Scholar
  2. Baltag A., Coecke B., Sadrzadeh M. (2007) Epistemic actions as resources. Journal of Logic and Computation 17(3): 555–585CrossRefGoogle Scholar
  3. Baltag, A., Moss, L. S., & Solecki, S. (1999). The logic of public announcements, common knowledge and private suspicions, CWI Technical Report SEN-R9922.Google Scholar
  4. Davey B.A., Priestley H.A. (1990) Introduction to lattices and order. Cambridge University Press, CambridgeGoogle Scholar
  5. Fagin, R., Halpern, J.Y., Moses, Y., & Vardi, M.Y. (1995). Reasoning about Knowledge. MIT Press.Google Scholar
  6. Gehrke M., Nagahashi H., Venema Y. (2005) A Sahlqvist theorem for distributive modal logic. Annals of Pure and Applied Logic 131: 65–102CrossRefGoogle Scholar
  7. Gerbrandy J. et al (1999) Dynamic Epistemic Logic. In: Moss L.S. (eds) Logic, Language, and Information 2. CSLI Publication, Stanford UniversityGoogle Scholar
  8. Hintikka J. (1962) Knowledge and belief: An introduction to the logic of two notions. Cornell University Press, New YorkGoogle Scholar
  9. Jonsson B., Tarski A. (1951) Boolean algebras with operators I. American Journal of Mathematics 73: 891–939CrossRefGoogle Scholar
  10. Jonsson B., Tarski A. (1952) Boolean algebras with operators II. American Journal of Mathematics 74: 127–162CrossRefGoogle Scholar
  11. Joyal, A., & Tierney, M. (1984). An extension of the Galois theory of Grothendieck. Memoirs of the American Mathematical Society, 309.Google Scholar
  12. Meyer J.J.C., van der Hoek W. (1995) Epistemic Logic for Computer Science and Artificial Intelligence, in Cambridge tracts in theoretical computer science, Vol. 41. Cambridge University Press, CambridgeGoogle Scholar
  13. Plaza, J. (1989). Logics of public communications. Proceedings of 4th International Symposium on Methodologies for Intelligent Systems.Google Scholar
  14. Sadrzadeh, M. (2005). Actions and Resources in Epistemic Logic, Ph.D. Thesis, University of Quebec at Montreal, http://www.ecs.soton.ac.uk/~ms6/all.pdf.
  15. van Benthem J. (1989) Logic in action. Journal of Philosophical Logic 20: 225–263CrossRefGoogle Scholar
  16. van Der Hoek, W., & Wooldridge, M. (2002). Time, knowledge, and cooperation: Alternating-time temporal epistemic logic, COORDINATION.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Laboratoire Preuves Programmes et SystèmesUniversité Paris DiderotParis 7France

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