Bounds to Memory Loss
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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