14.3 Derived Hypergraphs 273
corresponding to the presence of a certain pattern). The condition may refer to something in the world external to the system, or to something internal. For instance, the condition may be observing a cat. In this case, the corresponding Concept vertex in the mind of Ben Goertzel is the pattern of activity observed in Ben Goertzel’s brain when his eyes are open and he’s looking in the direction of a cat. The notion of pattern of activity can be made rigorous using mathematical pattern theory, as is described in The Hidden Pattern [Goe(6al.
Note that logical predicates, on the SMEPH level, appear as particular kinds of Concepts, where the condition involves a predicate and an argument. For instance, suppose one wants to know what happens inside Ben’s mind when he eats cheese. Then there is a Concept correspond- ing to the condition of cheese-eating activity. But there may also be a Concept corresponding to eating activity in general. If the Concept denoting the activity of eating X is generally eas- ily computable from the Concepts for X and eating individually, then the eating Concept is effectively acting as a predicate.
A SMEPH SchemaVertex, on the other hand, is like a Concept that’s defined in a time- dependent way. One type of Schema refers to a habitual dynamical pattern of activity occurring before and/or during some condition is met. For instance, the condition might be saying the word Hello. In that case the corresponding SchemaVertex in the mind of Ben Goertzel is the pattern of activity that generally occurs before he says Hello.
Another type of Schema refers to a habitual dynamical pattern of activity occurring after some condition X is met. For instance, in the case of the Schema for adding two numbers, the precondition X consists of the two numbers and the concept of addition. The Schema is then what happens when the mind thinks of adding and thinks of two numbers.
Finally, there are Schema that refer to habitual dynamical activity patterns occurring after some condition X is met and before some condition Y is met. In this case the Schema is viewed as transforming X into Y. For instance, if X is the condition of meeting someone who is not a friend, and Y is the condition of being friends with that person, then the habitually intervening activities constitute the Schema for making friends.
14.3.2 SMEPH Edges
SMEPH edge types fall into two categories: functional and logical. Functional edges connect Schema vertices to their input and outputs; logical edges refer mainly to conditional proba- bilities, and in general are to be interpreted according to the semantics of Probabilistic Logic Networks.
Let us begin with logical edges. The simplest case is the Subset edge, which denotes a straightforward, extensional conditional probability. For instance, it may happen that whenever the Concept for cat is present in a system, the Concept for animal is as well. Then we would say
Subset cat animal
(Here we assume a notation where “R A B” denotes an Edge of type R between Vertices A and On the other hand, it may be that 50% of the time that cat is present in the system, cute is present as well: then we would say
Subset cat cute <.5>
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