Reflective problem statements: the algebraic model

The paper is focused on reflective problematic statements presented by modal judgments of legitimacy (subjective truth) and their combinations. We propose a three-level model for describing reflective problematic statements: reflective problematic statements per se; modal judgments that define the legitimacy of sentences that form complex statements; matrix representations of modal judgments. Modal judgments as part of reflective problematic statements are hierarchically organized to form a “ladder of reflection”. We characterize the set of modal judgements that is isomorphic to a group of evaluation matrices of legitimacy. Along with the cognitive styles of personality, we determine personality cogital styles.