  A scheme for an algebraic quantization of the causal sets of Sorkin et al. is
presented. The suggested scenario is along the lines of a similar
algebraization and quantum interpretation of finitary topological spaces due to
Zapatrin and this author. To be able to apply the latter procedure to causal
sets Sorkin's `semantic switch' from `partially ordered sets as finitary
topological spaces' to `partially ordered sets as locally finite causal sets'
is employed. The result is the definition of `quantum causal sets'. Such a
procedure and its resulting definition is physically justified by a property of
quantum causal sets that meets Finkelstein's requirement from `quantum
causality' to be an immediate, as well as an algebraically represented,
relation between events for discrete locality's sake. The quantum causal sets
introduced here are shown to have this property by direct use of a result from
the algebraization of finitary topological spaces due to Breslav, Parfionov and
Zapatrin.
