Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 42

FIGURE 12. Nets of McCulloch formal neurons
computing the logical functions (a) “ A is equiva-
lent to B ” and (b) “either A or else B ”.
functions in Russell-Carnap symbols, while the sixth column translates it
into English.
The seventh, and last, column lists the “logical strength” Q of each func-
tion. According to Carnap (1938) it is possible to assign to each logical func-
tion a value which expresses the intuitive feeling for its strength as a logical
function. We intuitively consider a logical function to be weak if it is true
in most of the cases, irrespective of whether its arguments are true or false.
The tautology, which is always true, tells us nothing about the truth values
of its arguments. On the other hand, a function which is true only when all
its arguments are true we consider to be a strong logical function. Con-
sequently, as a measure of strength one may take the number of ways in
which the logical function is false. In other words, counting the number of
zeros in Wittgenstein's truth table gives the logical strength of the function.
Inspection of table 1 shows an interesting relationship between threshold