Axiomatizing Logics of False Belief and Radical Ignorance

The paper deals with the problem of axiomatizing the transitive logic of false belief, which was previously thought to be difficult. It proposes an "almost definability" schema that guides the discovery of core axioms for the transitive and Euclidean logics of false belief. It also introduces a suitable canonical relation that enables uniform completeness proofs for various logics of false belief, including the transitive logic. Furthermore, the paper extends the results to the logic of radical ignorance, showing that the operators of false belief and radical ignorance are interdefinable.