3.4 The General Structure of Cognitive Dynamics: Analysis and Synthesis 45 initial focus ( — (concepts, procedures, sm inference rules, etc.) : ee —_® ~~ if ra - a ort wa ™ combinations of items combinations of In nile OcuUS... e an combinations... Fig. 3.1: The General Process of Synthesis 3. Use the newly found constructions of the components in the current pool, to update the quantitative properties of the components in the current pool, and also (via the current pool) the quantitative properties of the components in the initial pool 4, Out of the components found in Step 2, select the ones that seem most promising according to the goal function, and add these to the current pool (or else simply define these as the current pool) 5. Return to Step 2 More formally, synthesis may be specified as follows. Let X denote the set of combinators, and let Yp denote the initial pool of components (the initial focus of the cognitive process). Given Y;, let Z; denote the set Reduce( Join(©;,(1), ...,C;)(r))) where the C; are drawn from Y; or from X. We may then say Yi41 = Filter(Z;) where Filter is a function that selects a subset of its arguments. Analysis, on the other hand, begins with a set W of components, and a set X of combinators, and tries to find a series Y; so that according to the process of synthesis, Y,=W. In practice, of course, the implementation of a synthesis process need not involve the explicit construction of the full set 7;. Rather, the filtering operation takes place implicitly during the construction of Y;,1. The result, however, is that one gets some subset of the compounds pro- ducible via joining and reduction from the set of components present in Y; plus the combinators Xx. HOUSE_OVERSIGHT_012961