Mark,
The basic inference rules in NARS that would support an implication of the
form S is a child of P are of the form:
DEDUCTION INFERENCE RULE:
Given S --> M and M--> P, this implies S --> P
ABDUCTION INFERENCE RULE:
Given S --> M and P --> M, this implies S --> P to some degree
INDUCTION INFERENCE RULE:
Given M --> S and M --> P, this implies S --> P to some degree
where "-->" is the inheritance relations.
Your arguments, are of the very different form :
Given P and Q, this implies Q --> P and P --> Q
And
Given S and R, this implies S --> R and R --> S
In the argument regarding drinking and being an adult, you do not
appear to use any of these NARS inference rules to show that P inherits
from Q or vice versa (unless, perhaps, one assumes multiple other NARS
sentences or terms that might help the inference along, such as an uber
category such as the category of all categories from which one could use
the abduction rule to imply both of the inheritances mentioned (which one
would assume the system would have learned over time was such a weak
source of implication as to be normally useless).
But in that example, just from common sense reasoning, including knowledge
of the relevant subject matter, (absent any knowledge of NARS) it appears
reasonable to imply P from Q and Q from P. So if NARS did the same it
would be behaving in a common sense way. Loops in transitivity might be
really ugly, but it seems any human-level AGI has to have the same ability
to deal with them as human common sense.
To be honest, I do not yet understand how implication is derived from the
inheritance relations in NARS. Assuming truth values of one for the child
and child/parent inheritance statement, I would guess a child implies its
parent with a truth value of one. I would assume a parent with a truth
value of one implies a given child with a lesser value that decrease the
more often the parent is mapped against other children.
The argument claiming NARS says that R ("most ravens are black") is both
the parent and child of S ("this raven is white") (and vice versa),
similarly does not appear to be derivable from only the statements given
using the NARS inference rules.
Nor does my common sense reasoning help me understand why most ravens are
black is both the parent and child of this raven is white. (All though
my common sense does tell me that this raven is black would provide
common sense inductive evidence for most ravens are black and that this
raven that is black would be a child of the category of most ravens
that are black.)
But I do understand that each of these two statements would tend to have
probabilistic effects on the other, as you suggested, assuming that the
fact a raven is black has implications on whether or not it is white. But
such two way probabilistic relationships are at the core of Bayesian
inference, so there is no reason why they should not be part of an AGI.
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 2:28 PM
To: [email protected]
Subject: Re: [agi] Do the inference rules of categorical logic make sense?
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
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. <mailto:[EMAIL PROTECTED]> Porter
To: [email protected]
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: [email protected]
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. <mailto:[EMAIL PROTECTED]> Porter
To: [email protected]
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 Wasers 10/9/2007 9:46 AM post: Perhaps Mark understands something
I dont.
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 siblings
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 NARSs inheritance (or categorizations) as being equivalent
two both of what I have considered two of the major dimensions in an AGIs
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 Goertzels 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 comps 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]>
mailto:[EMAIL PROTECTED]
Sent: Tuesday, October 09, 2007 9:46 AM
To: [email protected]
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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