  The causal structure of space-time offers a natural notion of an opposite or
orthogonal in the logical sense, where the opposite of a set is formed by all
points non time-like related with it. We show that for a general space-time the
algebra of subsets that arises from this negation operation is a complete
orthomodular lattice, and thus has several of the properties characterizing the
algebra physical propositions in quantum mechanics. We think this fact could be
used to investigate causal structure in an algebraic context. As a first step
in this direction we show that the causal lattice is in addition atomic, find
its atoms, and give necesary and sufficient conditions for ireducibility.
