Our general goal is to provide a semantic foundation for the specification of concurrent and distributed object systems. We use \sc Troll, a formal object-oriented language, for system specification. It is now widely accepted that object classes are unsuitable modularisation units when it comes to dealing with very large systems. An intermediate concept between the system and the objects is needed for allowing reusability of specifications and providing a clearer system structure. Enriching \sc Troll with a module concept forces us to develop new theoretical constructs ensuring an appropriate underpinning of the language. We propose a module logic \sc Mdtl for specifying and reasoning about the dynamic aspects of distributed and modular object systems. The main features of the logic include the ability to express module interaction and internal module concurrency. In this paper, we present the syntax and model-theoretic semantics of the module logic \sc Mdtl. The logic is illustrated and explained by means of a small toy example.