Sorry I have to be brief --- "Tuesday" means "5 hours teaching" to me. :-(
"Inheritance" mainly means (i.e., beside its formal definition) "to
use one term as another". If S --> P is true, then S inherits the
intension of P, and P inherits the extension of S; if it is true to a
degree, then the inheritance is partial, also to that degree.
"Similarity" is two-way inheritance. Implication/Equivalence mean to
use the truth value of one statement as the other, also to various
degrees.
To me, Inference/reasoning is not about "to find/prove the absolute
truth", but "to treat one thing (e.g., a novel object/situation) as
another (which is better known in experience)", and this is why I
think reasoning, when properly handled, is the core of intelligence.
Inheritance does not build a strict conceptual hierarchy, in the sense
that if S --> P then one is at a higher level than the other --- that
can be a special case, not a general case. I don't think concepts
should be put into such a hierarchy ("ontology"). A weaker type of
hierarchy is possible, such as to take "animal" to be at a higher
level than "human", but even in that case, "inheritance" can go the
other direction, as Lukasz pointed out.
On the other hand, compositional relations between compound terms and
component terms do form a strict hierarchy in Narsese, though the
situation is also not clear-cut. For example, in the paper on
categorization, I explained that in NARS the meaning of a compound
term may not be fully reducible to the meaning of its components.
Pei
On 10/9/07, Edward W. Porter <[EMAIL PROTECTED]> wrote:
>
>
>
> 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: [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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