Tableau Systems for Epistemic Positional Logics

The goal of the article is twofold. first one to provide logics based on positional semantics which will be suitable for analysis epistemic modalities such as ‘agent ... knows/beliefs that ...’. second define tableau systemsfor logics. Firstly, we present minimal logic MR. Then, change notion formulas and in order consider iterations operator realization “free” classical formulas. After that, move weaker avoid well known problem logical omniscience. At same time, keep counterparts modal axioms (T), (4) (5). For all considered sound complete systems.