McHenry, Leemon B.  "The Axiomatic Matrix of Whitehead's Process and Reality."  Process Studies 15, no. 3 (Fall 1986): 172-80.

Abstract

This paper investigates the mathematical background of Whitehead's metaphysical system.  It shows an affinity between Principia Mathematica and Process and Reality by the use of an "axiomatic matrix".  The common logical structure includes 1) a given operation or function, 2) a set of entities, 3) explanations of the primitive ideas, and 4) axioms as rules governing the relations between the entities.  Whitehead is not proceeding deductively in the metaphysics, but his setting out a definite statement of his first principles at the onset of his system indicates that he held the axiomatic method to be an ideal form in which one should strive to organize thought into a system.  [Abstract from The Philosopher's Index]