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Temporal Aspects of the Dynamics of Knowledge

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Johan van Benthem on Logic and Information Dynamics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 5))

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Abstract

Knowledge and time are fundamental aspects of agency and their interaction is in the focus of a wide spectrum of philosophical and logical studies. This interaction is two-fold: on the one hand, knowledge evolves over time; on the other hand, in the subjective view of the agent, time only passes when her knowledge about the world changes. In this chapter we discuss models and logics reflecting the temporal aspects of the dynamics of knowledge and offer some speculations and ideas on how the interaction of temporality and knowledge can be systematically treated.

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Notes

  1. 1.

    More generally, by varying the properties of the relation \(R\), these models can also represent other informational attitudes of the agent, such as beliefs.

  2. 2.

    This is somewhat more complicated in the asynchronous case, see [42, 44] for discussion and explanation.

  3. 3.

    To be more precise, \(\mathsf {R}_d\) is an event type (similarly for the other events in \(\varSigma \)).

  4. 4.

    The preconditions of DEL also encode protocol information of a ‘local’ character, and hence they can do some of the work of global protocols, as has been pointed out by van Benthem [12].

  5. 5.

    Note that this property may be violated even in an ETL model generated from only finitely many events.

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Acknowledgments

We thank Johan van Benthem, Joshua Sack and Dominik Klein for useful comments and references. Valentin Goranko’s work on this chapter was completed during his sabbatical visit to the Centre International de Mathématiques et Informatique de Toulouse. Eric Pacuit’s work was supported by an NWO Vidi Grant 016.094.345.

Author information

Authors and Affiliations

  1. Technical University of Denmark, 2800, Kongens Lyngby, Denmark

    Valentin Goranko

  2. University of Johannesburg, Auckland Park, Johannesburg, 2006, South Africa

    Valentin Goranko

  3. Department of Philosophy, University of Maryland, College Park, MD, USA

    Eric Pacuit

Authors
  1. Valentin Goranko
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Correspondence to Valentin Goranko .

Editor information

Editors and Affiliations

  1. University of Amsterdam Inst Logic,Language & Computation, Amsterdam, The Netherlands

    Alexandru Baltag

  2. Amsterdam, The Netherlands

    Sonja Smets

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Goranko, V., Pacuit, E. (2014). Temporal Aspects of the Dynamics of Knowledge. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_9

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