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246 13 Local, Global and Glocal Knowledge Representation
. Then we turn to distributed, neural-net-like knowledge representation, reviewing a host of
general issues related to knowledge representation in attractor neural networks, turning finally
to “glocal” knowledge representation mechanisms, in which ANNs combine localist and globalist
representation, and explaining the relationship of the latter to CogPrime. The glocal aspect of
CogPrime knowledge representation will become prominent in later chapters such as:
e in Chapter 23 of Part 2, where Economic Attention Networks (ECAN) are introduced and
seen to have dynamics quite similar to those of the attractor neural nets considered here,
but with a mathematics roughly modeling money flow in a specially constructed artificial
economy rather than electrochemical dynamics of neurons.
e in Chapter 42 of Part 2, where “map formation” algorithms for creating localist knowledge
from globalist knowledge are described
13.2 Localized Knowledge Representation using Weighted, Labeled
Hypergraphs
There are many different mechanisms for representing knowledge in AI systems in an explicit,
localized way, most of them descending from various variants of formal logic. Here we briefly
describe how it is done in CogPrime, which on the surface is not that different from a number of
prior approaches. (The particularities of CogPrime’s explicit knowledge representation, however,
are carefully tuned to match CogPrime’s cognitive processes, which are more distinctive in
nature than the corresponding representational mechanisms.)
13.2.1 Weighted, Labeled Hypergraphs
One useful way to think about CogPrime’s explicit, localized knowledge representation is in
terms of hypergraphs. A hypergraph is an abstract mathematical structure [Bol98], which con-
sists of objects called Nodes and objects called Links which connect the Nodes. In computer
science, a graph traditionally means a bunch of dots connected with lines (i.e. Nodes connected
by Links). A hypergraph, on the other hand, can have Links that connect more than two Nodes.
In these pages we will often consider “generalized hypergraphs” that extend ordinary hyper-
graphs by containing two additional features:
e Links that point to Links instead of Nodes
e Nodes that, when you zoom in on them, contain embedded hypergraphs.
Properly, such “hypergraphs” should always be referred to as generalized hypergraphs, but
this is cumbersome, so we will persist in calling them merely hypergraphs. In a hypergraph
of this sort, Links and Nodes are not as distinct as they are within an ordinary mathematical
graph (for instance, they can both have Links connecting them), and so it is useful to have a
generic term encompassing both Links and Nodes; for this purpose, we use the term Atom.
A weighted, labeled hypergraph is a hypergraph whose Links and Nodes come along with
labels, and with one or more numbers that are generically called weights. A label associated
with a Link or Node may sometimes be interpreted as telling you what type of entity it is, or
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