Approximations of modal logics: and beyond

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n -degree of introspection that is allowed, thus generating modal n -logics. The semantics for n -logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n -SST, and soundness and completeness is shown for the approximation of modal logics K,T,D,S4 and S5 .