We propose CoreTuLiP - the core of a trust management language based on Logic Programming. CoreTuLiP is based on a subset of moded logic programming, but enjoys the features of TM languages such as RT; in particular clauses are issued by different authorities and stored in a distributed manner. We present a lookup and inference algorithm which we prove to be correct and complete w.r.t. the declarative semantics. CoreTuLiP enjoys uniform syntax and the well-established semantics and is expressive enough to model scenarios which are hard to deal with in RT.