On 08/03/2017 10:06 AM, Linas Vepstas wrote:
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?
But isn't the same true for almost any link?
(Equivalence (stv 1 1) A (Or B C))
(And (stv 0 1) B C)
is immutable too, and could be equivalent to
(Partition (stv 1 1) A (Set B C))
saying that A is partitioned into block B and C.
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?
I agree about not creating new links up the wazzoo, it must be carefully
thought. However, you don't necessarily need to upgrade PLN to reason on
new links, if you can express the semantics of a new link as a
combination of old links, all you need is to write a higher order fact
such as
EquivalenceScope (stv 1 1)
$A $B $C
Partition $A (Set $B $C)
And
Equivalence $A (Or $B $C)
And $B $C
to enable PLN to reason about it.
Nil
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
<[email protected] <mailto:[email protected]>> wrote:
> Hi Ben, Mike,
>
> On Fri, Jul 21, 2017 at 9:41 PM, Ben Goertzel <[email protected]
<mailto:[email protected]>> 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
<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
>>
> --
> You received this message because you are subscribed to the Google Groups
> "opencog" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to [email protected]
<mailto:opencog%[email protected]>.
> To post to this group, send email to [email protected]
<mailto:[email protected]>.
> Visit this group at https://groups.google.com/group/opencog
<https://groups.google.com/group/opencog>.
> To view this discussion on the web visit
>
https://groups.google.com/d/msgid/opencog/CAHrUA35kQx%3DyDcLTynrThvi%3DrAVa15D-1PSwZpK_37Q%3DjZhcfw%40mail.gmail.com
<https://groups.google.com/d/msgid/opencog/CAHrUA35kQx%3DyDcLTynrThvi%3DrAVa15D-1PSwZpK_37Q%3DjZhcfw%40mail.gmail.com>.
> For more options, visit https://groups.google.com/d/optout
<https://groups.google.com/d/optout>.
--
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
--
You received this message because you are subscribed to the Google
Groups "opencog" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected]
<mailto:opencog%[email protected]>.
To post to this group, send email to [email protected]
<mailto:[email protected]>.
Visit this group at https://groups.google.com/group/opencog
<https://groups.google.com/group/opencog>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/opencog/CACYTDBdm6M1y18G%3DQi%3D_rjJcdrEb5eAmx8ntxffKoRw_dG1OYw%40mail.gmail.com
<https://groups.google.com/d/msgid/opencog/CACYTDBdm6M1y18G%3DQi%3D_rjJcdrEb5eAmx8ntxffKoRw_dG1OYw%40mail.gmail.com>.
For more options, visit https://groups.google.com/d/optout
<https://groups.google.com/d/optout>.
--
You received this message because you are subscribed to the Google
Groups "opencog" group.
To unsubscribe from this group and stop receiving emails from it, send
an email to [email protected]
<mailto:[email protected]>.
To post to this group, send email to [email protected]
<mailto:[email protected]>.
Visit this group at https://groups.google.com/group/opencog.
To view this discussion on the web visit
https://groups.google.com/d/msgid/opencog/CAHrUA34XVDQHNeYjb4r9eFjmrZxN%3DfNmE6wDQTV%2B__cJpEF3qw%40mail.gmail.com
<https://groups.google.com/d/msgid/opencog/CAHrUA34XVDQHNeYjb4r9eFjmrZxN%3DfNmE6wDQTV%2B__cJpEF3qw%40mail.gmail.com?utm_medium=email&utm_source=footer>.
For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups
"opencog" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/opencog.
To view this discussion on the web visit
https://groups.google.com/d/msgid/opencog/8aa12595-28a0-f983-be51-db8c8d3719c3%40gmail.com.
For more options, visit https://groups.google.com/d/optout.
