This paper studies the laws of communicating sequential processes (CSP) with Z-like initial and final states. Instead of defining a large semantics including all observable aspects, we incrementally develop the model in three stages: partially correct relational model, then totally correct sequential model and finally the reactive-process model with states. The properties of each model are captured as algebraic laws. A law in one model may or may not be true in its submodels. We apply a technique based on healthiness conditions to identify the conditions for law inheritance. Such abstract conditions themselves can be captured as pattern laws of commutativity. The model uses a new approach to define parallel compositions using just the primitive commands, nondeterministic choice, conjunction and some unary (hiding) operators.
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