The Minkowski causal logic, which is already known to be a complete or
thomodular lattice, is found to be also an atomistic and irreducible l
ogic, but to have no other essential properties to be represented in t
erms of all the subspace of some Hilbert space. Alternative representa
tion of the logic in terms of subspaces of a real vector space or of t
he states in terms of probability measures are suggested.