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Bounds to Memory Loss

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  • Hans Hvide

Abstract

If we express our knowledge in sentences, we will find that these sentences to some extent are linked by logical rules. We ask whether the structure logic imposes on our knowledge restricts what we forget and what we remember. The model is a two period S5-style modal logic. In this logic we propose a memory loss operator: The agent forgets a sentence p if and only if he knows p at time 1 and he does not know p at time 2. Equipped with the operator, we prove theorems on the relation between knowledge and memory loss. The main results point to classes of formulas that an agent cannot forget, and classes of formulas he must forget. A desirable feature is that most results hold in the S4 logic. The results illustrate bounds to memory loss, and thus to bounded rationality. We apply the model to single-agent conventions: Conventions made between an agent and himself.
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Suggested Citation

  • Hans Hvide, 1999. "Bounds to Memory Loss," Theory and Decision, Springer, vol. 46(1), pages 1-21, February.
    • Handle: RePEc:kap:theord:v:46:y:1999:i:1:p:1-21
    DOI: 10.1023/A:1004942613175
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    References listed on IDEAS

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    Cited by:

    1. Nicola Dimitri, 2005. "Dynamic Consistency in Extensive form Decision Problems," Department of Economics University of Siena 455, Department of Economics, University of Siena.
    2. Hvide, Hans K., 2002. "Pragmatic beliefs and overconfidence," Journal of Economic Behavior & Organization, Elsevier, vol. 48(1), pages 15-28, May.

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    More about this item

    Keywords

    Bounded rationality; Imperfect recall; Memory loss operator; Redundancy; Reasoning through time; S5 logic; Single-agent conventions;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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