MessageMost of the discussion I read in Pei's article related to inheritance
relations between terms, that operated as subject and predicates in sentences
that are inheritance statements, rather than between entire statements, unless
the statement was a subject or a predicate of a higher order inheritance
statement. So what you are referring to appears to be beyond what I have read.
Label the statement "I am allowed to drink alcohol" as P and the statement "I
am an adult" as Q. P implies Q and Q implies P (assume that age 21 equals
adult) --OR-- P is the parent of Q and Q is the parent of P.
Label the statement that "most ravens are black" as R and the statement that
"this raven is white" as S. R affects the probability of S and, to a lesser
extent, S affects the probability of R (both in a negative direction) --OR-- R
is the parent of S and S is the parent of R (although, realistically, the
probability change is so miniscule that you really could argue that this isn't
true).
NARS's inheritance is the "inheritance" of influence on the probability values.
----- Original Message -----
From: Edward W. Porter
To: agi@v2.listbox.com
Sent: Tuesday, October 09, 2007 1:12 PM
Subject: RE: [agi] Do the inference rules of categorical logic make sense?
Mark,
Thank you for your reply. I just ate a lunch with too much fat (luckily
largely olive oil) in it so, my brain is a little sleepy. If it is not too
much trouble could you please map out the inheritance relationships from which
one derives how "I am allowed to drink alcohol" is both a parent and the child
of "I am an adult." And could you please do the same with how "most ravens are
balck" is both parent and child of "this raven is white."
Most of the discussion I read in Pei's article related to inheritance
relations between terms, that operated as subject and predicates in sentences
that are inheritance statements, rather than between entire statemens, unless
the statement was a subject or a predicate of a higher order inheritance
statement. So what you are referring to appears to be beyond what I have read.
Edward W. Porter
Porter & Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
-----Original Message-----
From: Mark Waser [mailto:[EMAIL PROTECTED]
Sent: Tuesday, October 09, 2007 12:47 PM
To: agi@v2.listbox.com
Subject: Re: [agi] Do the inference rules of categorical logic make sense?
Thus, as I understand it, one can view all inheritance statements as
indicating the evidence that one instance or category belongs to, and thus is
"a child of" another category, which includes, and thus can be viewed as "a
parent" of the other.
Yes, that is inheritance as Pei uses it. But are you comfortable with the
fact that "I am allowed to drink alcohol" is normally both the parent and the
child of "I am an adult " (and vice versa)? How about the fact that "most
ravens are black" is both the parent and child of "this raven is white" (and
vice versa)?
Since inheritance relations are transitive, the resulting hierarchy of
categories involves nodes that can be considered ancestors (i.e., parents,
parents of parents, etc.) of others and nodes that can be viewed as descendents
(children, children of children, etc.) of others.
And how often do you really want to do this with concepts like the above --
or when the evidence is substantially less than unity?
And loops and transitivity are really ugly . . . .
NARS really isn't your father's inheritance.
----- Original Message -----
From: Edward W. Porter
To: agi@v2.listbox.com
Sent: Tuesday, October 09, 2007 12:24 PM
Subject: RE: [agi] Do the inference rules of categorical logic make sense?
RE: (1) THE VALUE OF "CHILD OF" AND "PARENT OF" RELATIONS & (2)
DISCUSSION OF POSSIBLE VALUE IN DISTINGUISHING BETWEEN GENERALIZATIONAL AND
COMPOSITIONAL INHERITANCE HIERARCHIES.
Re Mark Waser's 10/9/2007 9:46 AM post: Perhaps Mark understands
something I don't.
I think relations that can be viewed as "child of" and "parent of" in a
hierarchy of categories are extremely important (for reasons set forth in more
detail below) and it is not clear to me that Pei meant something other than
this.
If Mark or anyone else has reason to believe that "what [Pei] means is
quite different" than such "child of" and "parent of" relations, I would
appreciate being illuminated by what that different meaning is.
My understanding of NARS is that it is concerned with inheritance
relations, which as I understand it, indicate the truth value of the assumption
that one category falls within another category, where category is broadly
defined to included not only what we normally think of as categories, but also
relationships, slots in relationships, and categories defined by a sets of one
or more properties, attributes, elements, relationships, or slot in
relationships. Thus, as I understand it, one can view all inheritance
statements as indicating the evidence that one instance or category belongs to,
and thus is "a child of" another category, which includes, and thus can be
viewed as "a parent" of the other. Since inheritance relations are transitive,
the resulting hierarchy of categories involves nodes that can be considered
ancestors (i.e., parents, parents of parents, etc.) of others and nodes that
can be viewed as descendents (children, children of children, etc.) of others.
I tend to think of similarity as a sibling relationship under a shared
hidden parent category -- based on similar aspects of the sibling's extensions
and/or intensions.
In much of my own thinking I have thought of such categorization
relations as is generalization, in which the parent is the genus, and the child
is the species. Generalization is important for many reasons. First,
perception is trying to figure which in category or generalization of things,
actions, or situations various parts of a current set of sensory information
might fit. Secondly, Generalization is important because it is necessary for
implication. All those Bayesian probabilities we are used to thinking about
such as P(A|B,C), are totally useless unless we have some way of knowing the
probability the situation being considered contains a B or C. To do that you
have to have categories that help you determine the extent to which a B or a C
is present. To understand the implication of P(A|B,C) you have to have some
meaning for the category A. Generalization is important for behavior because
one uses generalization learned from past experiences to develop plans for how
to achieve goals, and because most action schema are usually generalization
that have to be instantiated in a context specific way.
One of the key problems in AI has been non-literal matching. That is why
representation schemes that have a flexibility something like that of NARS are
necessary for any intelligence capable of operating well in anything other than
limited domains. That is why so-called "invariant" or "hierarchical memory"
representations are so valuable. This is indicated in writings of Jeff
Hawkins, Thomas Serre ("Learning a Dictionary of Shape-Components in Visual
Cortex: Comparison with Neurons, Humans and Machines", by Thomas Serre, the
google-able article I have cited so many times), and many others. Such
hierarchical representations achieve their flexibility though a
composition/generalization hierarchy which presumably maps easily into NARS.
Another key problem in AI is context sensitivity. A hierarchical
representation scheme that is capable of computing measures of similarity, fit,
and implications throughout multiple levels in such a hierarchical
representation scheme of multiple aspects of a situation in real time can be
capable of sophisticated real time context sensitivity. In fact, the ability
to perform relative extensive real time matching and implication across
multiple levels of compositional and generalization hierarchies has been a key
feature of the types of systems I have been thinking of for years.
That is one of the major reasons why I have argued for "BREAKING THE
SMALL HARDWARE MINDSET."
I understand NARS's inheritance (or categorizations) as being equivalent
two both of what I have considered two of the major dimensions in an AGI's self
organizing memory, (1) generalization/similarity and (2) composition. I was,
however, aware, that down in the compositional (comp) hierarchy can be viewed
as up in the generalization (gen) hierarchy, since the set of things having one
or more properties or elements of a composition can be viewed as a
generalization of that composition (i.e., the generalization covering the
category of things having that one or more properties or elements).
Although I understand there is an importance equivalence between down in
the comp hierarchical and up in the gen hierarchy, and that the two could be
viewed as one hierarchy, I have preferred to think of them as different
hierarchies, because the type of gens one gets by going up in the gen hierarchy
tend to be different than the type of gens one gets by going down in the comp
hierarchy.
Each possible set in the powerset (the set of all subsets) of elements
(eles), relationships (rels), attributes (atts) and contextual patterns
(contextual pats) could be considered as possible generalizations. I have
assumed, as does Goertzel's Novamente, that there is a competitive ecosystem
for representational resources, in which only the fittest pats and gens -- as
determined by some measure of usefulness to the system -- survive. There are
several major uses of gens, such as aiding in perception, providing inheritance
of significant implication, providing appropriate level of representation for
learning, and providing invariant representation in higher level comps.
Although temporary gens will be generated at a relatively high frequency,
somewhat like the inductive implications in NARS, the number of gens that
survive and get incorporated into a lot of comps and episodic reps, will be an
infinitesimal fraction of the powerset of eles, rels, atts, and contextual
features stored in the system. Pats in the up direction in the Gen hierarchy
will tend to be ones that have been selected for the usefulness as
generalizations. They will often have reasonable number of features that
correspond to that of their species node, but with some of them more broadly
defined. The gens found by going down in the comp hierarchy are ones that have
been selected for their representational value in a comp, and many of them
would not normally be that valuable as what we normally think of as
generalizations.
In the type of system I have been thinking of I have assumed there will
be substantially less multiple inheritance in the up direction in the gen
hierarchy than in the down direction in the comp hierarchy (in which there
would be potential inheritance from every ele, rel, att, and contextual feature
of in a comp's descendant nodes at multiple levels in the comp hierarchy below
it. Thus, for spreading activation control purposes, I think it is valuable to
distinguish between generalization and compositional hierarchies, although I
understand they have an important equivalence that should not be ignored.
I wonder if NARS makes such a distinction.
These are only initial thoughts. I hope to become part of a team that
gets an early world-knowledge computing AGI up and running. Perhaps when I do
feedback from reality will change my mind.
I would welcome comments, not only from Mark, but also from other
readers.
Edward W. Porter
Porter & Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
-----Original Message-----
From: Mark Waser [mailto:[EMAIL PROTECTED]
Sent: Tuesday, October 09, 2007 9:46 AM
To: agi@v2.listbox.com
Subject: Re: [agi] Do the inference rules of categorical logic make
sense?
> I don't believe that this is the case at all. NARS correctly
> handles
> cases where entities co-occur or where one entity implies another only
due
> to other entities/factors. "Is an ancestor of" and "is a descendant
of"
> has nothing to do with this.
Ack! Let me rephrase. Despite the fact that Pei always uses the words
of
inheritance (and is technically correct), what he means is quite
different
from what most people assume that he means. You are stuck on the
"common"
meanings of the terms "is an ancestor of" and "is a descendant of" and
it's
impeding your understanding.
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