Minimal model semantics for nonmonotonic modal logics

Intuitively clear Kripke-style semantics for nonmonotonic modal logic are provided. Minimal model semantics is defined, and soundness and completeness of the semantics for nonmonotonic modal logics are proved. It is shown how the semantics looks for some most popular or most interesting modal logics. Applications to finding expansions and comparing nonmonotonic logics based on different monotonic modal logics are presented. A few examples of using the semantics for obtaining intuitively clear proofs of some results of nonmonotonic modal logics are given