Logics of False Belief and Reliable Belief

In the literature, the question regarding how to axiomatize the transitive logic of false belief is thought of as hard and left as an open problem. In this paper, among other contributions, we deal with this problem. In more detail, although the standard doxastic operator is undefinable with the operator of false belief, the former is almost definable with the latter. On one hand, the involved almost definability schema guides us to find the desired core axioms for the transitive logic and the Euclidean logic of false belief. On the other hand, inspired by the schema and other considerations, we propose a suitable canonical relation, which can uniformly handle the completeness proof of various logics of false belief, including the transitive logic. We also extend the results to the logic of reliable belief, due to the interdefinability of the operators of false belief and reliable belief.