Abstract
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 pif and only if he knows pat time 1 and he does not know pat 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Bacharach, M. and Mongin, P. (1994), Epistemic logic in game theory, Theory and Decision37: 1-24.
Battigalli, P. and Bonanno, G. (1997), The logic of belief persistency (draft).
Bergson, H. (1919), The Spiritual Energy. PUF-Quadrige 1985 edition.
Dow, J. (1991), Search decisions with limited memory, Review of Economic Studies58: 15-41.
Fagin, R., Halpern, J. Y., Moses, Y. and Vardi, M. Y. (1995), Reasoning about Knowledge. The MIT Press.
Gärdenfors, P. (1988), Knowledge in Flux. The MIT Press.
Haack, S. (1978), Philosophy of Logics. Cambridge University Press.
Halpern, J. Y. (1986), Reasoning about knowledge: an overview, Theoretical Aspects of Reasoning about Knowledge, vol. I. Morgan Kaufman Publishers.
Hintikka,. (1962), Knowledge and Belief. Cornell University Press.
Hughes, G. E. and Creswell, M. J. (1968), An Introduction to Modal Logic. Methuen Press.
Hvide, H. K. (1997), Self-awareness, uncertainty, and markets with overconfidence. NHH discussion paper 9/97.
Kaneko, M. and Nagashima, T. (1996), Game logic and its applications I, Studia Logica57: 325-54.
Kaneko, M. and Nagashima, T. (1997), Game logic and its applications II, Studia Logica58(2): 273-303.
Lemmon, E. J. (1959), Is there only one correct System of Modal Logic?, Proceedings of the Aristotelian Society33: 23-44.
Lipman, B. L. (1995), Information processing and bounded rationality: a survey Canadian Journal of Economics38: 42-67.
Modica, S. and Rustichini, A. (1994), Awareness and partitional information structures, Theory and Decision37: 107-124.
Piccione, M. and Rubinstein, A. (1997), On the interpretation of decision problems with imperfect recall, forthcoming in Games and Economic Behaviour.
Shoham, Y. (1989), Time for action, Proceedings, 11th International Joint Conference on Artificial Intelligence, pp. 954-959.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hvide, H.K. Bounds to Memory Loss. Theory and Decision 46, 1–21 (1999). https://doi.org/10.1023/A:1004942613175
Issue Date:
DOI: https://doi.org/10.1023/A:1004942613175