On Fri, Aug 4, 2017 at 3:07 AM, Nil Geisweiller <ngeis...@googlemail.com>
wrote:

> 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?
>

No. I think you're missing the point. Equivalence is normally between pairs
of things, and that is very manageable.  You can say a=b and say b=c and
then later change your mind about b=c without affecting a=b at all.  That
is very different than saying {a,b,c} is an equivalence-set.

That is, the atomspace is optimized for relations between pairs of things,
or maybe triples. quadruple-relations are very rare.  By contrast, sets
with hundreds or thousands or millions of members are not uncommon.

We are not the first to deal with this.  So both SQL and no noSQL are  are
both very explicitly be a "relational algebras", and are very explicitly
not "set theories". In SQL, the table forms a "set", and it is very easy to
add/remove rows in that set. A single row is a relation.  The table of
employees has one row per employee. It does NOT have all of the employees
jammed into one big giant arbitrary-length row.


>
> (Equivalence (stv 1 1) A (Or B C))
> (And (stv 0 1) B C)
>

Both AndLink and OrLink are set-like in their behavior, and this is a
problem.  They are not relational, as currently defined.

In SQL, And and Or's are handled between rows, (as inner/outer joins) and
not within the same row.


>
> 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.
>

I don't want to argue about it here, but I think that turning everything
explicitly into a scope link is a minor mistake.  I think it's just fine to
have scoping be implicit.  We don't need to invent a brand new
BlahScopeLink for each and every BlahLink.   Just pretend that BlahLink is
a BlahScopeLink with zero variables. That's all. Don't special-case zero
variables as being different from more-than-zero variables.

--linas

>
> 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
>>     <linasveps...@gmail.com <mailto:linasveps...@gmail.com>> wrote:
>>      > Hi Ben, Mike,
>>      >
>>      > On Fri, Jul 21, 2017 at 9:41 PM, Ben Goertzel <b...@goertzel.org
>>     <mailto: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
>>     <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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