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A mathematical definition of classical causality over discrete spacetimedynamics is formulated. The approach is background free and permits adefinition of causality in a precise way whenever the spacetime dynamicspermits. It gives a natural meaning to the concepts of cosmic time, spacelikehypersurfaces and timelike or lightlike flows without assuming the notion of abackground metric. The concepts of causal propagators and the speed ofcausality are discussed. In this approach the concepts of spacetime anddynamics are linked in an essential and inseparable whole, with no meaning toeither on its own.

Discrete spacetime: classical causality,prediction, retrodiction and the mathematical arrow of time