Distributed Peer-to-Peer and Grid infrastructure require distributed access control mechanisms. These mechanisms can be implemented in distributed trust management infrastructures and usually require reasoning on more than one peer, as soon as authority is delegated or requests involve several authorities. Building on previous work of the authors which formalized such a distributed trust management infrastructure based on distributed logic programs, we describe in this paper how reasoning can be implemented as distributed logic evaluation and how loops during this evaluation can be handled with. Our solution is based on a loop tolerant distributed tabling algorithm which includes in the process protection of sensitive policies and generation of proofs without increasing the complexity of the system.