Process Grammar

Abstract

This report gives an exposition of the Process-Grammar, published originally in the journalArtificialIntelligencein 1988, together with a description of some of the subsequent applications of thegrammar in meteorology, biology, computer-aided design, chemical engineering, and geology. TheProcess-Grammar is a means of recovering the process-history of a smooth shape from its curvatureextrema, and expressing that evolution in terms of transitions at those extrema. The inference ofhistory follows from the Symmetry-Curvature Duality Theorem of Leyton (1987), which states that,to each curvature extremum, there is a differential symmetry axis leading to and terminating at thatextremum; and from an inference rule that states that the symmetry axis is the record of a process.The Process-Grammar expresses the relationship between any two stages in the shape’s history asan extrapolation of the processes inferred by the theorem.