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A Simple-Minded Network Model with Context-like Objects - Bruce Edmonds

4 An enhanced network model

The basic model comprises of a set of labelled nodes and directed arcs. Unlike usual networks, directed arcs can go from node to another arc as well as from node to node. I will call this an extended net. An example is shown below in
figure 1. Arcs such as the one in figure 1 between the tweety node and the bird node which are not pointed to by a directed arcs, I will call an unconditional arc. Other arcs (such as the one from the bird to the flyer node) will be called conditional arcs.

Figure 1: Example of an extended net

The simple idea is that nodes and arcs are either activated or not. The activation of one node can cause unconditional arcs leading from it to be activated. Conditional arcs may be activated if the node they lead from is activated and any arc leading to it is active. Nodes are activated by activated arcs leading to it. The spreading of activation from one node to another represents an inference. Chains of activated arcs will be called a path. There are various possible elaborations of this scheme, but I will leave these to later (section 5).

Nodes that have many paths leading from it to other arcs then act like a context. If they are activated they enable many inferences to occur that would not be possible otherwise. I will call such nodes contextual nodes. Note: I am not claiming these are contexts or that they model real properties of natural contexts but just that they have context-like features.

Context-dependent learning could take place when there are a number of "background" facts associated with the induced/observed connection. For example, when walking into an aviary one may be aware that it is a specialised enclosure designed for keeping birds, in that aviary one may observe that all the birds fly. Here an association between birds and flight is made in the context of the group of properties that distinguish the situation one finds oneself in (see figure 2). Later one may separately learn to distinguish the relevant features of an aviary.

Figure 2: Learning that birds fly in the context of an aviary

Since nodes representing contexts are just as other nodes, they can themselves easily be part of an inference network. This allows the next context to be selected base on the previous context and other information. Contexts need not be in a strict hierarchy. Contexts may be active one at a time or multipley. Contexts can have a specific identity as in the aviary example shown in figure 2 above, where the collection of context related facts have been abstracted to that of an aviary.

Generalisation of facts from a set of specific contexts to a more general one can be done by learning common associations in several related contexts. There are many possible schema for generalisation expressible using this model. One such is shown in figure 3 below; here there is an arc (A to B) shared between two contexts, C1 and C2, (alternatively they may be duplicated - that is a matter of the semantics of the formalisation), the condition of this arc may then be generalised to a wider context (GC).

Figure 3: a possible schema for generalisation from specific contexts

Due to limitations of space I have not described the possible processing of these networks in any detail, of which there are several possibilities.

A Simple-Minded Network Model with Context-like Objects - Bruce Edmonds - 13 FEB 97
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