3.6 Postscript: Formalizing Pattern 53

3.6 Postscript: Formalizing Pattern 53 Specific Objects Abstract Concepts Composite Actions, (Some corresponding to Perception Action Complex Feelings named concepts, some not) & . - US Feeling Nodes f pixel at (100,50) is RED at 1:42:01, Sept 15,2006 joint_53_actuator is ON at 2:42:01, Sept 15, 2006 Fig. 3.4: Graphical depiction of the momentary bubble of attention in the memory of an OpenCog AI system, a few moments after the bubble shown in Figure 3.3, indicating the mov- ing of the bubble of attention. Depictive conventions are the same as in Figure 1. This shows an idealized situation where the declarative knowledge remains invariant from one moment to the next but only the focus of attention shifts. In reality both will evolve together. 3.6 Postscript: Formalizing Pattern Finally, before winding up our very brief tour through patternist philosophy of mind, we will briefly visit patternism’s more formal side. Many of the key aspects of patternism have been rigorously formalized. Here we give only a few very basic elements of the relevant mathematics, which will be used later on in the exposition of CogPrime. (Specifically, the formal definition of pattern emerges in the CogPrime design in the definition of a fitness function for “pattern min- ing” algorithms and Occam-based concept creation algorithms, and the definition of intensional inheritance within PLN.) We give some definitions, drawn from Appendix 1 of [Goe06a];: Definition 1 Given a metric space (M,d), and two functions c: M — [0,co| (the “simplicity measure”) and F: M —> M (the “production relationship”), we say that P © M is a pattern in X € M to the degree HOUSE_OVERSIGHT_012969