Imperfect-recall, Evidential Partition, and Monty Hall

Philosophical arguments for the rationality of Bayesian conditioning often use assumptions and concepts from epistemic logic without fully explicating them. In this work, we present a general dynamic epistemic logic framework to analyze logical properties of (Bayesian) learning scenarios. We argue that Perfect-Recall is an important epistemic principle at the heart of the project of justifying Bayesian conditioning. In such epistemic logic formulation, Perfect-Recall is not really about memory, but about the agent’s general ability to know how they came to know what they know. Following the existing literature, we use Monty Hall style cases to demonstrate the connection between Perfect-Recall and the commitments of Bayesian conditioning.