On Tue, Aug 1, 2017 at 1:24 AM, Ben Goertzel <b...@goertzel.org> wrote:
> Hi Linas,
>
> The difference between PartitionLink and MemberLink is pretty obvious,
> right?
Not to me ... I realize now that perhaps you mean "SubSetLink" and I
thought we had one of those, but perhaps it has different semantics. See
below.
> A PartitionNode defines a partition of the set denoted by a
> ConceptNode. The partition elements that are linked to the
> PartitionNode by a PartitionLink can of course also be linked via a
> MemberLink to the ConceptNode that corresponds to the PartitionNode.
> However, the unique semantics of a partition is that of mutual
> exclusivity and completeness, i.e. the intersection between two
> distinct elements of the partition is null, and the union of the
> elements of the partition is the set being partitioned.
OK. well .. where, exactly, does my hip end, and my body start?
In intro-to-diff-geom there is a concept of "partition of unity" which is a
collection of functions that sum up to one. and each one individually
smoothly interpolates between zero and one. They indicate a general area.
They do NOT have a null intersection -- they can have a big huge sloppy
intersection, but that works just fine because they have derivatives that
cancel out (because the derivative of one is zero).
Practically, a problem with partitions is, what do you do if you forget to
specify one of the parititions? should one assume that the unspecified part
is "everything else?"
There's also a problem of editing: what if, half-way through, you want to
change the partition? Can you? should you? should users instead be told
that a partition, once-created, is immutable, so you can only create and
destroy them?
Do you truly need a partition link? I mean - I invent new link types all
the time, since that's usually pretty cheap. But I also do not expect my
new link types to work with PLN. In this case, don't you want pln interop?
An alternate way of thinking about partitions is as "coloring". Pick a set,
pick N colors, and then insist that every member of the set must be colored
with one of the N colors. Then coloring is a lot like partitioning. e.g.
ColorLink
ColorNode "Red"
SomeAtom
or maybe
EvaluationLink
ColorNode "red"
SomeAtom
Color names could, of course, be anything: e.g. the names of the
partitions.
In one sense, colorings are identical to partitions; on the other hand,
they can feel "more general" because you can insist or demand that certain
properties of colorings hold, e.g. ramsey theory and reverse mathematics.
You could *force* aka gaurantee uniqueness of color assignment by using a
StateLink:
StateLink
Some Atom
ColorNode "red"
The atomspace automatically gaurantees that one and only one color can be
assigned. (although it can be changed) The UniqueLink allows only one
assignment, and it cannot be changed. These are nice, because they help
avoid programmer error. by offering automatic guarantees.
You don't have to use atoms for this, either. You could use values.
Recall, values are almost just like atoms, except that you can't put them
into the atomspace, and you cannot pattern-match or patttern-mine them.
But you can store color or partition data in values, if you wanted to.
Note that values *can* hold atoms! There is a LinkValue that is like a
link, but it can hold atoms or values or a mixture of both.
--linas
> This
> semantics is implicit in PartitionNode, whereas if you just use
> MemberLink you'd need to spell out this "partition" semantics using a
> bunch of AndLinks each time...
>
> As a world-class advocate of the partition function I think you may
> like PartitionNode after you reflect on it infinitesimally more...
>
> -- ben
>
> On Tue, Aug 1, 2017 at 5:54 AM, Linas Vepstas <linasveps...@gmail.com>
> wrote:
> > Hi Ben, Mike,
> >
> > On Fri, Jul 21, 2017 at 9:41 PM, Ben Goertzel <b...@goertzel.org> wrote:
> >>
> >> Some interesting representational issues have come up in the context
> >> of Atomspace representation of pathways, which appear to have more
> >> general implications…
> >>
> >> It seems the semantics we want for a biological pathway is sort of
> >> like “the pathway P is a set of relationships R1, R2, …, R20” in kinda
> >> the same sense that “the human body is a set of organs: brain, heart,
> >> lungs, legs, etc.”
> >>
> >> First of all it seems what we have here is a part of relationship… maybe
> >> we want
> >>
> >> PartLink
> >> ConceptNode “heart”
> >> ConceptNode “human-body”
> >>
> >> and
> >>
> >> PartLink
> >> >relationship<
> >> >pathway<
> >>
> >> PartLink and PartOfLink have come and gone in
> >> OpenCog/Novamente/Webmind history...
> >>
> >> An argument that PartLink should have fundamental status and a
> >> well-defined fuzzy truth value is given in this paper:
> >>
> >> https://www.academia.edu/1016959/Fuzzy_mereology
> >>
> >> However what we need for biological pathways and human bodies seems
> >> like a bit more. We want to say that a human body consists of a
> >> certain set of parts... not just that each of them is a part... We're
> >> doing a decomposition.
> >>
> >> One way to do this would be
> >>
> >> PartitionLink
> >> ConceptNode “human-body”
> >> ListLink
> >> ConceptNode “legs”
> >> ConceptNode “arms”
> >> ConceptNode “brain”
> >> etc.
> >>
> >> Relatedly, we could also have
> >
> >
> > As mentioned earlier, there are several problems with this format. One
> is
> > the "oops I forgot to mention xyz in the list" or "gosh I should have
> left
> > out pqr" and this becomes a big problem: you have to delete the
> > PartitionLink, delete the ListLink, create a new list and partition. In
> the
> > meanwhile, some other subsystem might be holding a handle to the old,
> > now-wrong PartitionLink, and there is no effective way of announcing "hey
> > stop using that old thing, get my new thing now".
> >
> > A second problem is that the above doesn't have anywhere to hang
> addtional
> > data: e.g. "legs are a big part of the human body, having a mas of nearly
> > half of the body." You can't just slap that on as a (truth)value, cause
> > there's no where to put that value.
> >
> > Third problem is that large list-links are hard to handle in the pattern
> > matcher. Its much much harder to write a query of the form "find me all
> > values of $X where
> >
> > PartitionLink
> > ConceptNode “human-body”
> > ListLink
> > ConceptNode “legs”
> > VariableNode “$X”
> > ConceptNode “brain”
> >
> > because, ... well the ListLink is an ordrerd link, not an unordered
> link. If
> > you forget to include the pqr (added above) then the search will fail.
> You
> > could try to use unordered links and globnodes, but these lead to other
> > difficulties, including the n! possible permutations of an unordered link
> > become large n-factorial large when the unordered link has n items in it.
> > Recall that old factorial-70 trick used to make calculators overflow.
> >
> > In general, any link with more than 3 or 4 or 5 items in it is bad news.
> > This is a generic statement about knowledge representation in opencog.
> >
> >
> >> OverlappingPartitionLink
> >> C
> >> L
> >>
> >> if we want to encompass cases where the partition elements in L can
> >> overlap; or
> >>
> >> CoveringLink
> >> C
> >> L
> >>
> >> if we want to encompass cases where the partition elements in L can
> >> overlap, AND the elements in L may encompass some stuff that’s not in
> >> C
> >>
> >> For the pathway case, we could then say
> >>
> >> PartitionLink
> >> ConceptNode “Krebs cycle”
> >> ListLink
> >> >relationship 1<
> >> >relationship 2<
> >> etc.
> >>
> >>
> >> Now this solves the semantics problem but doesn’t solve the problem of
> >> having a long ListLink…. A biological pathway might have 100s or
> >> 1000s of relationships in it, and we don't usually want to make lists
> >> that big in the Atomspace...
> >>
> >> To solve this we could do something like (for the human body case)
> >>
> >> PartitionLink
> >> ConceptNode “human-body”
> >> PartitionNode “body-partition-1”
> >>
> >> PartitionElementLink
> >> PartitionNode “body-partition-1"
> >> ConceptNode “legs”
> >>
> >> PartitionElementLink
> >> PartitionNode “body-partition-1"
> >> ConceptNode “arms”
> >>
> >> etc.
> >>
> >> and similarly (for the biological pathway case)
> >>
> >> PartitionLink
> >> ConceptNode “Krebs cycle”
> >> PartitionNode “krebs-partition-1”
> >>
> >> PartitionElementLink
> >> PartitionNode “krebs-partition-1"
> >> >relationship 1<
> >>
> >> PartitionElementLink
> >> PartitionNode “krebs-partition-1”
> >> >relationship 2<
> >
> >
> >
> > Yeah, sure. Not sure why the existing MemberLink is not sufficient for
> your
> > purposes. The MemberLink has reasonably-well-defined semantics, there are
> > already rules for handling it in PLN (or there will be rules -- I think
> its
> > something Nil has thought about) I'm not clear on why you'd want to
> invent
> > something that is just like MemberLink but is different.
> >
> >>
> >>
> >> ...
> >>
> >> There could be some nice truth value math regarding these, e.g. we
> >> could introduce Ellerman's "logical entropy" which is really a
> >> partition entropy. There are also connections with some recent
> >> theoretical work I've been doing on "graphtropy" (using "distinction
> >> graphs" that generalize partitions), which I'll post a paper on
> >> sometime in the next week or two.... But that will be another email
> >> for another day...
> >
> >
> > Yeah graphical-entropy is something that I keep trying to work on, except
> > that every new urgent disaster of the day distracts me from it.
> >
> > --linas
> >>
> >>
> >> -- Ben
> >>
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>
>
> --
> Ben Goertzel, PhD
> http://goertzel.org
>
> "I am God! I am nothing, I'm play, I am freedom, I am life. I am the
> boundary, I am the peak." -- Alexander Scriabin
>
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