Bounds to Memory Loss

Posted: 24 Mar 2000

See all articles by Hans K. Hvide

Hans K. Hvide

University of Bergen - Department of Economics; University of Aberdeen - Business School; Centre for Economic Policy Research (CEPR); Institute for the Study of Labor (IZA)


If we express our knowledge in sentences, we will find that these sentences are linked in complex patterns governed by our observations and our inferences from these observations. These inferences are to a large extent driven 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 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 future versions of himself.

JEL Classification: C00, D80

Suggested Citation

Hvide, Hans, Bounds to Memory Loss. Available at SSRN:

Hans Hvide (Contact Author)

University of Bergen - Department of Economics ( email )

Fosswinckelsgt. 6
N-5007 Bergen, 5007

University of Aberdeen - Business School ( email )

Edward Wright Building
Dunbar Street
Aberdeen, Scotland AB24 3QY
United Kingdom


Centre for Economic Policy Research (CEPR)

United Kingdom

Institute for the Study of Labor (IZA) ( email )

P.O. Box 7240
Bonn, D-53072

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