Soggy predicates

[Ben Goertzel]

Nil, Amen, does the below seem to you to summarize our conversation on
Soggy predicates last week? or did I forget something?

ben


***

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])

(Note that the set of observations O need not be the observations
actually made by the AI system whose memory contains the predicate —
it may be observations made by some other hypothesized entities, etc.)

In this case we have a clear interpretation for

EvaluationLink <s>
PredicateNode F
Atom x

So we can say

PredicateNode F <t>

means the average degree to which an arbitrary element y of the AI
system’s “default set of observations” satisfies F (i.e. the average
over this default observation-set of F(y))…

Or, for an observation-set C, we can say

ContextLink <t1>
ConceptNode C
PredicateNode F

where t1 is the average over F(y), where y is counted in the average
with a weight proportional to the degree to which y is in C.

So then

PredicateNode F <t>

means, conceptually,

ContextLink <t>
>default context<
PredicateNode F

Next, we can then define

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.

This becomes slightly subtle to interpret in the case that the
argument of F is a list.

For example,

EvaluationLink <s>
PredicateNode “eat”
ListLink
ConceptNode “cat”
ConceptNode “mouse”

converts to

ExtensionalInheritanceLink <s>
ListLink
ConceptNode “cat”
ConceptNode “mouse”
SatisfyingSet
ConceptNode “eat”

which means that s is the average degree to which an observation (in
the default overall observation-set) involving “eat”, also involves
the pair (eater = cat, eatee=mouse).


--
Ben Goertzel, PhD
http://goertzel.org

“I tell my students, when you go to these meetings, see what direction
everyone is headed, so you can go in the opposite direction. Don’t
polish the brass on the bandwagon.” – V. S. Ramachandran

[Ben Goertzel]

Pasted to wiki at

http://wiki.opencog.org/w/Soggy_Predicates

[Nil Geisweiller]

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

[Nil Geisweiller]

On 01/13/2017 03:26 PM, Nil Geisweiller wrote:
> 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])

I guess what I would have written is:

"
For each x, the number F(x) lies in [0,1] and can be interpreted as the
average degree to which an arbitrary element of x, some set of
observations, has property F. (Here we assume that the degree to which a
specific observation has a property F is itself a number in [0,1])
"

So replaced O by x, then it makes complete sense, and don't even need to
bring up the formal definition.

Nil