I just remembered that I never announced this paper in which I was trying to learn some concurrency theory. It depends on a note on representation, that used to be its appendix. It will be available soon. The ps-file with A4-format is in papers/Pavlovic on theory.doc.ic.ac.uk; the American format is in pub/pavlovic on triples.math.mcgill.ca. All the best, -- Dusko CATEGORICAL LOGIC OF CONCURRENCY AND INTERACTION I: SYNCHRONOUS PROCESSES by Dusko Pavlovic (August 1994) Abstract. This is a report on a mathematician's effort to understand some concurrency theory. The starting point is a logical interpretation of Nielsen and Winskel's account of the basic models of concurrency. Upon the obtained logical structures, we build a calculus of relations which yields, when cut down by bisimulations, Abramsky's interaction category of synchronous processes. It seems that all interaction categories arise in this way. The obtained presentation uncovers some of their logical contents and perhaps sheds some more light on the original idea of processes as relations extended in time. The sequel of this paper will address the issues of asynchronicity, preemption, noninterleaving and linear logic in the same setting.