PROBLEMS OF FORMALISATION OF KNOWLEDGE IN EPISTEMIC MODAL LOGIC
We made a revision of epistemic modal logics formalizing knowledge judgments in the article. Special attention is paid to the omniscience problem and to the different types of solving it in modal epistemic logic. The analysis showed that we could form two general types of epistemic logics, which try to overcome the omniscience problem in the epistemic modal logic. The first type of epistemic logic solves omniscience problem by reducing deductive capacities of agents. The second one solves it by introduction of additional operator interpreted as mental efforts, which are necessary to deduce new knowledge expressed in logic formulae. We prove that it is necessary to introduce meaning gaps in the system of epistemic modal logic to express a lack of knowledge in some world. We offer to build an epistemic three-digit logic, the third meaning will be a meaning gap.