This study proposes a logic-based security policy framework. First, the study proposes the security policy syntax and semantic. Next, four algoritms are proposed to transfer first-order logic based security policies into extended logic programs to evaluate queries with simple goals, to transfer complex queries into simple ones, and to verify security policies against complex security properties. Under well-founded semantics, all the algorithms are sound and completed, and their computational complexities are polynomial. In this framework, security policy declaration, evaluation and verification are executed under the same semantics, which is significant for security policy management. Furthmore, the framework can manage the security policies with advanced features, such as non-monotony and recursion, which is not supported in many existent security policy management frameworks.