272 14 Representing Implicit Knowledge via Hypergraphs

272 14 Representing Implicit Knowledge via Hypergraphs e Concept Vertex, representing a set, for instance, an idea or a set of percepts e SchemaVertex, representing a procedure for doing something (perhaps something in the physical world, or perhaps an abstract mental action). The key SMEPH Edge types, using language drawn from Probabilistic Logic Networks (PLN) and elaborated in Chapter 34 below, are as follows: e ExtensionalInheritanceEdge (ExtInhEdge for short: an edge which, linking one Vertex or Edge to another, indicates that the former is a special case of the latter) e ExtensionalSimilarityEdge (ExtSim: which indicates that one Vertex or Edge is similar to another) e ExecutionEdge (a ternary edge, which joins $,B,C when S is a SchemaVertex and the result from applying S to B is C). So, in a SMEPH system, one is often looking at hypergraphs whose Vertices represent ideas or procedures, and whose Edges represent relationships of specialization, similarity or transforma- tion among ideas and/or procedures. The semantics of the SMEPH edge types is given by PLN, but is simple and common- sensical. ExtInh and ExtSim Edges come with probabilistic weights indicating the extent of the relationship they denote (e.g. the ExtSimEdge joining the cat ConceptVertex to the dog ConceptVertex gets a higher probability weight than the one joining the cat Concept Vertex to the washing-machine ConceptVertex). The mathematics of transformations involving these probabilistic weights becomes quite involved - particularly when one introduces SchemaVertices corresponding to abstract mathematical operations, a step that enables SMEPH hypergraphs to have the complete mathematical power of standard logical formalisms like predicate cal- culus, but with the added advantage of a natural representation of uncertainty in terms of probabilities, as well as a natural representation of networks and webs of complex knowledge. 14.3 Derived Hypergraphs We now describe how SMEPH hypergraphs may be used to model and describe intelligent systems. One can (in principle) draw a SMEPH hypergraph corresponding to any individual intelligent system, with Vertices and Edges for the concepts and processes in that system’s mind. This is called the derived hypergraph of that system. 14.3.1 SMEPH Vertices A ConceptVertex in the derived hypergraph of a system corresponds to a structural pattern that persists over time in that system; whereas a SchemaVertex corresponds to a multi-time- point dynamical pattern that recurs in that system’s dynamics. If one accepts the patternist definition of a mind as the set of patterns in an intelligent system, then it follows that the derived hypergraph of an intelligent system captures a significant fraction of the mind of that system. To phrase it a little differently, we may say that a ConceptVertex, in SMEPH, refers to the habitual pattern of activity observed in a system when some condition is met (this condition HOUSE_OVERSIGHT_013188