The paper puts forward a new logical theory—free modal description theory LK which is the abbreviation of LFMDTK.The theory’s theoretical background,formal language,grammatical system and corresponding semantics are given.We prove the soundness of LK.By forcing method and constructing forcing model,we prove the system’s completeness in the end.Contrasting with other free description theories,one of important features of LK is that it introduces the modal operator "necessity".So it can deal with the case that definite description appears in the modal context.The essential difference between individual constant,individual variable and definite description is reflected in the system.Individual constant and individual variable are rigid designator,while definite description is not.
