Epistemic States Guiding the Rational Dynamics of Information

Abstract

An epistemic state here means a total preorder on the set of possible worlds. Simple epistemic states, with one or two equivalence classes, correspond to belief sets. Relative to a fixed belief set t, we define a comparative order on belief sets, expressing that ‘y sorts the worlds closer to the way in which t sorts them than x does’. This induces a Boolean algebra, ordered very differently from, but isomorphic to the Lindenbaum-Tarski algebra under the isomorphism which sends x to x↔ t. The isomorphism allows us to classify each inferential or conjectural step as being either in concord or in discord with the beliefs t. So t may now guide the logical dynamics of inference and conjecture, and hence of corroboration, refutation, diagnosis, abduction, etc. Going from belief sets to more general epistemic states, we show how similar constructions may guide AGM belief change.