This paper studies logic based methods for representing and evaluating complex access control policies needed by modern database applications. In our framework, authorization and delegation rules are specified in a Weighted Delegatable Authorization Program (WDAP) which is an extended logic program. We show how extended logic programs can be used to specify complex security policies which support weighted administrative privilege delegation, weighted positive and negative authorizations, and weighted authorization propagations. We also propose a conflict resolution method that enables flexible delegation control by considering priorities of authorization grantors and weights of authorizations. A number of rules are provided to achieve delegation depth control, conflict resolution, and authorization and delegation propagations.