Detection of a global predicate is a fundamental problem in distributed computing. In this paper we describe new predicate detection algorithms for certain temporal logic predicates. We use a temporal logic, CTL, for specifying properties of a distributed computation and interpret it on a finite lattice of global states. We present solutions to the predicate detection of linear and observer-independent predicates under EG and AG operators of CTL. For linear predicates we develop polynomial-time predicate detection algorithms which exploit the structure of finite distributive lattices. For observer-independent predicates we prove that predicate detection is NP-complete under EG operator and co-NP-complete under AG operator. We also present polynomial-time algorithms for a CTL operator 'called until' for which such algorithms did not exist. Finally, outwork unifies many earlier results in predicate detection in a single framework.