I found that the passage from logic to algebra is actually pretty easy.
The key step being the unification step:
h x = f
where h is the head of the rule, f is a fact, x is a set of substitutions
to be solved for. This can be represented in a vector space.
The problem is that my formulas exist in a *discrete* space. Consider 2
formulas:
A. "JFK was assassinated by a lone gunner"
B. "JFK was killed by CIA conspiracy"
There is no way to move *continuously* from A to B, unless we allow
discrete "jumps".
One of Ben's ideas is to assign probability distributions over all possible
formulas. That way, the distributions over A and B vary smoothly, they
form a manifold whose distance metric is given by the K-L divergence
between 2 probability distributions.
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AGI
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