This paper introduces a formalism named SINC aimed at the design and verification of synchronous concurrent systems. The components of this formalism are a transition system and a first-order linear-time temporal logic. The SINC transition system adopts a synchronous computation model, includes a method to solve write-conflicts, and represents transitions as possibly non-terminating imperative commands. The SINC logic allows for formal reasoning about SINC transition systems using compositional and modular proofs. Such features are important to the verification of a large class of systems, but they are missing in other formalisms based on transition systems and temporal logics. This paper also discusses some of the pragmatics in specifying and verifying systems using SINC, and presents extensions to deal with generic parameters and regular structures. SINC is based on the Hoare logic and the UNITY formalism.