On the logic of conscious belief

Abstract

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (Bα ≡ BBα and ∼ Bα ≡ B ∼ Bα) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.