Ben,

I only read it now, see my comments below.

On 12/14/2016 04:40 AM, Ben Goertzel wrote:
A Simple Observation Grounded predicate, or Soggy predicate, is an
uncertain predicate F so that: For each x, the number F(x) lies in
[0,1] can be interpreted as the average degree to which an arbitrary
element of some set O of observations has property x.   (Here we
assume that the degree to which a specific observation has a property
x is itself a number in [0,1])

OK, but I think the definition for F(O) is missing, right?

I guess formally what we want is, given a universe U, define an extension of F:U->[0,1] to PowerSet(U) such that

F(O) = weighted average of F(x) over O

or formally

F(O).s = Sum_x F(x).s * (Member x O).s / Sum_x (Member x O).s

right?

EvaluationLink <s>
    PredicateNode F
    Atom x

as being equivalent to

MemberLink <s>
    Atom x
    SatisfyingSet
       PredicateNode F

Basically, this is just defining the membership function of the fuzzy set

    SatisfyingSet
       PredicateNode F

in a particular way.

We can then convert this ("M2I rule") to

ExtensionalInheritanceLink <s>
    Atom x
    SatisfyingSet
       PredicateNode F

because of the way F was originally defined.

Yes, this entails from the definition of the extension of F to PowerSet(U).

Apart from that formal omission, it's all clear. I'll add to the wiki the definition of F extension, unless you disagree, then let me know why.

Nil

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