Scholastic Logic of "Knowledge" V. Systems of Epistemic Logic

The study aims at the systematic presentation of basic systems of scholastic epistemic logic (regardless of its original distribution into different contexts and genres). Scholastic epistemic logic can be (re)interpreted as a conservative extension of a certain non-modal base, which can be viewed as the model of epistemic agents. Its fundamental principles are: [O] if 4 implies psi and an agent knows that 4, then the agent knows that psi; [T] if an agent knows that 4, then 4; [K] if an agent knows that 4implies psi and that 4, then the agent knows that psi; [4] an agent who knows 4 knows to know 4; [5] an agent who fails to know 4knows to fail to know 4; (or their modifications). From this point of view, scholastic epistemic logic can be construed as a confrontation of logical systems with unequal strength, ranging between that of John Wyclif, Peter of Mantua and Paul of Venice, William Heytesbury, and finally (a different theory of) Paul of Venice. These systems represent the hierarchy of epistemic agents by extending the set of their basic properties, including veridicality, inferential extendability, and introspectibility of knowledge.