Revisable Justified Belief: Preliminary Report

The theory CDL of Conditional Doxastic Logic is the single-agent version of Board’s multi-agent theory BRSIC of conditional belief. CDL may be viewed as a version of AGM belief revision theory in which Boolean combinations of revisions are expressible in the language. We introduce a theory JCDL of Justified Conditional Doxastic Logic that replaces conditional belief formulas Bφ by expressions t :φ made up of a term t whose syntactic structure suggests a derivation of the belief φ after revision by ψ. This allows us to think of terms t as reasons justifying a belief in various formulas after a revision takes place. We show that JCDL-theorems are the exact analogs of CDL-theorems, and that this result holds the other way around as well. This allows us to think of JCDL as a theory of revisable justified belief.