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Semantics for Knowledge and Change of Awareness

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Abstract

We examine various logics that combine knowledge, awareness, and change of awareness. An agent can become aware of propositional propositions but also of other agents or of herself. The dual operation to becoming aware, forgetting, can also be modelled. Our proposals are based on a novel notion of structural similarity that we call awareness bisimulation, the obvious notion of modal similarity for structures encoding knowledge and awareness.

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Notes

  1. In van Ditmarsch and French (2011), \(K_i^S\) was called introspective knowledge and written as \(K_i\).

References

  • Baltag, A., Moss, L., & Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In I. Gilboa (Ed.), Proceedings of 7th TARK (pp. 43–56). Morgan Kaufmann.

  • Board, O., & Chung, K. S. (2009). Object-based unawareness: Theory and applications. Technical report, University of Minnesota, Department of Economics.

  • Browne, M., Clarke, E., & Grümberg, O. (1987). Characterizing Kripke structures in temporal logic. In H. Ehrig, R. Kowalski, G. Levi, & U. Montanari (Eds.), TAPSOFT ’87, LNCS 249 (pp. 256–270). Springer.

  • d’Agostino, G., & Hollenberg, M. (2000). Logical questions concerning the \(\mu \)-calculus: Interpolation, Lyndon and Los-Tarski. Journal of Symbolic Logic, 65(1), 310–332.

    Article  Google Scholar 

  • Fagin, R., & Halpern, J. (1988). Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1), 39–76.

    Article  Google Scholar 

  • Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge, MA: MIT Press.

    Google Scholar 

  • Fine, K. (1970). Propositional quantifiers in modal logic. Theoria, 36(3), 336–346.

    Article  Google Scholar 

  • French, T. (2006). Bisimulation quantifiers for modal logic. Ph.D. thesis, University of Western Australia.

  • Grossi, D., & Velázquez-Quesada, F. (2009). Twelve angry men: A study on the fine-grain of announcements. In X. He, J. Horty, & E. Pacuit (Eds.), Proceedings of 1st LORI (pp. 147–160). Springer, LNCS 5834.

  • Halpern, J., & Rego, L. (2009). Reasoning about knowledge of unawareness. Games and Economic Behavior, 67(2), 503–525.

    Article  Google Scholar 

  • Heifetz, A., Meier, M., & Schipper, B. (2006). Interactive unawareness. Journal of Economic Theory, 130, 78–94.

    Article  Google Scholar 

  • Hill, B. (2010). Awareness dynamics. Journal of Philosophical Logic, 39, 113–137.

    Article  Google Scholar 

  • Hintikka, J. (1962). Knowledge and belief. Ithaca, NY: Cornell University Press.

    Google Scholar 

  • Hollenberg, M. (1998). Logic and bisimulation. Ph.D. thesis, University of Utrecht.

  • Levesque, H. (1984). A logic of implicit and explicit belief. In R. Brachman (Ed.), Proceedings of AAAI (pp. 198–202). AAAI Press.

  • Lin, F., & Reiter, R. (1994). Forget it!. In Proceedings of AAAI fall symposium on relevance (pp. 154–159). New Orleans.

  • Meyer, J. J., & van der Hoek, W. (1995). Epistemic logic for AI and computer science (Vol. 41). Cambridge University Press, Cambridge Tracts in Theoretical Computer Science.

  • Modica, S., & Rustichini, A. (1994). Awareness and partitional information structures. Theory and Decision, 37, 107–124.

    Article  Google Scholar 

  • Modica, S., & Rustichini, A. (1999). Unawareness and partitional information structures. Games and Economic Behavior, 27, 265–298.

    Article  Google Scholar 

  • Plaza, J. (1989). Logics of public communications. In M. Emrich, M. Pfeifer, M. Hadzikadic, & Z. Ras (Eds.), Proceedings of the 4th ISMIS (pp. 201–216). Oak Ridge National Laboratory.

  • Stirling, C. (1998). The joys of bisimulation. In Brim, L., Gruska, J., & Zlatuska, J. (Eds.), Mathematical foundations of computer science 1998 (Proceedings of 23rd international symposium) (pp. 142–151). Springer, LNCS 1450.

  • van Benthem, J. (1998). Dynamic odds and ends. Technical report, University of Amsterdam, ILLC Research, Report ML-1998-08.

  • van Ditmarsch, H., & French, T. (2009a). Awareness and forgetting of facts and agents. In P. Boldi, G. Vizzari, G. Pasi, & R. Baeza-Yates (Eds.), Proceedings of WI-IAT workshops 2009 (pp. 478–483). IEEE Press.

  • van Ditmarsch, H., & French, T. (2009b). Simulation and information. In J. Broersen & J. J. Meyer (Eds.), Knowledge Representation for Agents and Multi-Agent Systems (pp. 51–65). Springer, LNAI 5605.

  • van Ditmarsch, H., & French, T. (2011). Becoming aware of propositional variables. In M. Banerjee & A. Seth (Eds.), Proceedings of 4th ICLA (pp. 204–218). Springer, LNCS 6521.

  • van Ditmarsch, H., Herzig, A., Lang, J., & Marquis, P. (2009). Introspective forgetting. Synthese (Knowledge, Rationality and Action), 169(2), 405–423.

    Google Scholar 

  • van Ditmarsch, H., French, T., & Velázquez-Quesada, F. (2012). Action models for knowledge and awareness. In W. van der Hoek, L. Padgham, V. Conitzer, M. Winikoff (Eds.), Proceedings of 11th AAMAS (pp. 1091–1098).

  • van Ditmarsch, H., French, T., Velázquez-Quesada, F., & Wang, Y. (2013). Knowledge, awareness, and bisimulation. In B. Schipper (Ed.), Proceedings of 14th TARK (pp. 61–70).

  • van Eijck, J., & Sietsma, F. (2011). Message-generated Kripke semantics. In K. Tumer, P. Yolum, L. Sonenberg, P. Stone (Eds.), Proceedings of 10th AAMAS (pp. 1183–1184).

  • Velázquez-Quesada, F. (2011). Small steps in dynamics of information. Ph.D. thesis, University of Amsterdam, ILLC dissertation series DS-2011-02.

  • Velázquez-Quesada, F. (2013). Expressivity hierarchy of languages for epistemic awareness models. In D. Grossi, O. Roy, & H. Huang (Eds.), Proceedings of 4th LORI (pp. 253–266). Springer LNCS 8196.

  • Visser, A. (1996). Bisimulations, model descriptions and propositional quantifiers. Logic Group Preprint Series 161, Department of Philosophy, Utrecht University.

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Acknowledgments

We thank the reviewers of the journal for their comments. Discussion with participants of ICLA Delhi were helpful to pursue this research. We wish to thank Thomas Ågotnes for encouraging us. Hans van Ditmarsch is also affiliated with the Institute of Mathematical Sciences Chennai (IMSC), India, as associated researcher. This research is supported by European Research Council Grant EPS 313360.

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Authors and Affiliations

  1. LORIA—CNRS, University of Lorraine, Vandoeuvre Les Nancy, France

    Hans van Ditmarsch

  2. University of Western Australia, Perth, Australia

    Tim French

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  1. Hans van Ditmarsch
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  2. Tim French
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Correspondence to Hans van Ditmarsch.

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van Ditmarsch, H., French, T. Semantics for Knowledge and Change of Awareness. J of Log Lang and Inf 23, 169–195 (2014). https://doi.org/10.1007/s10849-014-9194-z

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