DRM technology is becoming one of the critical techniques to protect digital rights in the Internet. Rights expression languages (RELs) in DRM system are languages devised to construct licenses and describe usage rights of digital content. Most of current rights expression languages are based on XML, which lack a formal semantics and when the conditions of user become complex, the syntax of the languages are complicated and obscure. Due to the problems, the rights expression language LucScript is presented, which is a language based on logical framework that owns logical advantages of expressiveness, flexibility and semantic integrity to XML-based languages. The logic semantic, syntax and triggering mechanism of the language framework are analyzed and explained. And the implementation mechanism of the language is discussed. Finally, the application and process of usage control of the language are exampled. The language is based on integral semantics of Active-U-Datalog that owns a unique stable model, which makes the language own more expressiveness and flexibility than other logic-based rights expression languages. A comparative analysis between LucScript and LicenseScript language which owns the most powerful expressiveness at the present time is also shown at the end of the paper. LucScript language can improve usage flexibility and capability of real-time control of digital content in DRM system effectively.