Categories & the Geometry of Mind (Facebook Group)
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On Mon, Jan 27, 2014 at 4:33 AM, YKY (Yan King Yin, 甄景贤) <
[email protected]> wrote:
> 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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