Paper ID: 2402.15445

Can we forget how we learned? Doxastic redundancy in iterated belief revision

Paolo Liberatore

How information was acquired may become irrelevant. An obvious case is when something is confirmed many times. In terms of iterated belief revision, a specific revision may become irrelevant in presence of others. Simple repetitions are an example, but not the only case when this happens. Sometimes, a revision becomes redundant even in presence of none equal, or even no else implying it. A necessary and sufficient condition for the redundancy of the first of a sequence of lexicographic revisions is given. The problem is coNP-complete even with two propositional revisions only. Complexity is the same in the Horn case but only with an unbounded number of revisions: it becomes polynomial with two revisions. Lexicographic revisions are not only relevant by themselves, but also because sequences of them are the most compact of the common mechanisms used to represent the state of an iterated revision process. Shortening sequences of lexicographic revisions is shortening the most compact representations of iterated belief revision states.

Submitted: Feb 23, 2024