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Mechanization of Cognition 59

confabulation), is that a lexicon can have multiple highly excited symbols at the end of a
confabulation (as opposed to just one active symbol or the null symbol). When this occurs, the
neurons representing these symbols will be excited at various (high) levels for different symbols.
When such multiple highly excited but not active symbols are used as ‘‘assumed facts’’
transmitting through a knowledge base, their effects on symbols to which they link via this
knowledge base will essentially be the product of their excitation times, the link strength.
In practice, such multi-symbol ‘‘assumed facts’’ are very important, as they are the key ingre-
dients in consensus building (dynamically interacting confabulations taking place contemporan-
eously in multiple lexicons), which is the dominant mode of use of confabulation in human
cognition. However, to keep this chapter at an elementary and introductory level, the mathematics
of multiple-symbol ‘‘assumed fact sets’’ will not be discussed in detail. As needed, the qualitative
properties of this mode of confabulation will be discussed, which will be sufficient for this
introduction.
For the technological purposes of this chapter, confabulation will be taken to be dependent upon
the input excitation sum I(l) of symbol l, which is redefined (from the Appendix) to be:

I(l) [ln (p(ajl)=p ) þ B] þ [ln (p(bjl)=p ) þ B] þ [ln (p(gjl)=p ) þ B]
0 0 0
þ [ln (p(djl)=p ) þ B]
0
¼ ln [p(ajl) p(bjl) p(gjl) p(djl)] 4ln (p ) þ 4B, (3:1)
0
where ln is the natural logarithm function, B is a positive global constant called the bandgap
(a term coined by my colleague Robert W. Means), and p 0 is the smallest meaningful p(cjl) value.
Clearly, for a symbol l receiving N knowledge links, the value of I(l) ranges over the numerical
interval from NBto N[ln(1/p 0 ) þ B]. It will be assumed that the constant B is selected such that for
N ¼ 1, 2, . . . , N max none of these intervals ever overlap. For example, if we take p 0 ¼ 0.0005 and
N max ¼ 10, then we can select B ¼ 100. The intervals upon which I(l) can lie are then given by
[100,107.6], [200,215.2], . . . , [1000,1076.0] for N ¼ 1, 2, . . . , N max , respectively. The utility of
this definition will be seen immediately below. Given these preliminaries, we can now discuss
variants of confabulation.
The first effect considered is erasing, denoted by E. Erasing clears the current record of
excitation states of the lexicon and prepares the lexicon for a new use. For example, before a
lexicon is used as the answer lexicon of a confabulation operation, it must be erased.
Elementary confabulation (as described in Hecht-Nielsen, 2005), denoted by W, is carried out
by activating a single symbol e with the highest value of I(l) (ties are broken randomly). By
activation it is meant that the final excitation level I(e) of that symbol is set to 1 and the final
excitation levels of all other symbols are set to zero. There is also the effect WK, which is the same
as W with the added requirement that the single winning symbol, if there is to be one, must have had
at least K knowledge link inputs (i.e., the winning symbol must have its input intensity in the Kth,
or higher, I(l) interval). The primary form of confabulation discussed in Hecht-Nielsen (2005)
was W4.
The effect CK (confabulation conclusions having K or more knowledge link inputs), which will
be needed for discussions, first zeros the excitation sum I(u) of each symbol u whose I(u) is not in the
Kth (or higher) I(l) interval(s) occupied by symbols of the lexicon. The excitation levels of all
the symbols are then summed. Finally, each remaining nonzero symbol excitation is then divided
by this sum to yield its final excitation level. For example, in the above example with p 0 ¼ 0.0005
and N max ¼ 10, and B ¼ 100, if the four highest symbol input excitation sums are 346.8, 304.9,
225.0, and 146.8, then a C2 will yield only the top three symbols, with final excitation levels of
0.395, 0.3478, and 0.2566, respectively. Clearly, this effect yields the set of confabulation conclu-
sion symbols that had K or more knowledge link inputs. Normalizing the sum of the ‘‘significant
symbol’s’’ excitation levels to 1.0 corresponds to the notions of ‘‘activation’’ and ‘‘high excitation’’