This paper presents a supremal-control generalization of a temporal version of supervisory control for temporal-safety in discrete-event systems. The generalization is an outcome of the development of a temporal logic equations approach formulated using unary transformer concepts borrowed mainly from the predicate and predicate transform theory of Dijkstra and Scholten. The proposed syntax-based approach has not hitherto been formally augmented to the temporal logic framework, and is shown to parallel and to generalize the boolean equations approach proposed in the existing predicate control theory of Kumar, Garg and Marcus. A detailed example, which cannot be handled by the existing predicate control theory, demonstrates how the natural language basis of temporal logic for requirement specification and syntax-based control synthesis can be unified in a common logic framework. (c) 2005 Elsevier Ltd. All rights reserved.