On Tue, Aug 8, 2017 at 2:37 AM, Nil Geisweiller <ngeis...@googlemail.com>
wrote:

>
> However I don't think the more "atomic" representation should replace the
> more "holistic" one, both should be allowed in parallel, right? Would that
> be for backward compatibility at least. Then if it becomes obvious that the
> atomic form is superior we can deprecate the holistic form.
>

I've personally concluded that in many, most cases, using SetLink is a
complete disaster. Again -- look at SQL as an example. You *could* create a
table that places all employees on a single row. The language supports
this. But every textbook written on it will explain why this would be
exactly the wrong way of doing things, and then talk about "normalization"
for the next 6 chapters.

Same deal here: I am saying that, in general, we should be careful, and
apply good-practices to knowledge-base design. Read the books on knowledge
bases, study the concept of data normalization, data orthogonality, and
avoid making those kind of mistakes, when designing structures for opencog.

I didn't notice it at first, but now I do: relex2logic, sureal and
microplanning abuse SetLink. Not sure what the rule-engine is doing, but I
suspect its abusing to too. The people who designed SQL were smart, it took
them a decade+ to figure this shit out, and we should not abandon their
good advice for random, willy-nilly reasons.  We should avoid repeating
old, well-known mistakes.


>     EquivalenceScope (stv 1 1)
>>        <vardecl>
>>        P
>>        Q
>>
>>     is merely sugar syntax for
>>
>>     Equivalence (stv 1 1)
>>        Lambda <vardecl> P
>>        Lambda <vardecl> Q
>>
>>     This sugar syntax is mostly useful for humans, because <vardecl> is
>>     not duplicated in the AtomSpace anyway.
>>
>>
>> Well, but that's not true!  (Scope X   P(X)==Q(X)) is not the same as
>> (Scope X  P(X)) == (Scope X  Q(X)) because the latter can be
>> alpha-rewritten as (Scope X  P(X)) == (Scope Y  Q(Y)) which is something
>> completely different!
>>
>
> Agreed, they're not the same in the logic that you describe, but in PLN
> they are, because the former
>
> (Scope X   P(X)==Q(X))
>
> is just *syntactic sugar* for the latter,
>
> (Scope X  P(X)) == (Scope X  Q(X))
>

You keep saying that, but I don't see how it can possibly be true. It is
always, 100% legal to rewrite Scope X  P(X)) == (Scope X  Q(X)) as  (Scope
X  P(X)) == (Scope Y  Q(Y)) and, in classical logic, they have completely
different meanings.

let P(x) == "x can fly"   and Q(x) == "x has two legs"

then  (Scope X   P(X)==Q(X))  means "x has two legs and can fly"

which might or might not be true, depending on the value of x. while

(Scope X  P(X)) == (Scope y  Q(y)) means "the statement that  "x can fly"
is identical to the statement that "y has two legs"

which is clearly always false. (and cannot depend on the values for x,y)
Now, there might be models which that statement is true: for example, on
planet nimrod, all flying things have two legs, and all two-legged things
fly.  Thus, planet nimrod is a "model" where that statement is true.
However, the "theory" that (Scope X  P(X)) == (Scope y  Q(y)) is still
false on planet nimrod, even though the model is true. I think maybe you
are failing to distinguish theories and models? they are not the same
thing....


> which is what really matters in a probabilistic interpretation.
>

OK, so perhaps they are equal in PLN, its just that they are not equal in
general.

The formal way of saying this is that two models of a theory might be
equal, but this does not mean the two theories are equal.  Its the
difference between equality and equivalence: two things can be
"accidentally" equal and not be equivalent.

Here, PLN would be one possible model, classical logic is another possible
model, Bayesian probability a third possible model.  The truth value of a
statement can be different in each of these different  models, and is not,
in general, the same as the truth value of a statement in a theory.

It is the case that when something is true in a theory, then it is also
true in every model of that theory.  So for example,

let P(x) == "x can fly"   and Q(x) == "x has property of flight"

Then (Scope X  P(X)) == (Scope y  Q(y)) is true as a theory, always, and so
it had also better always be true in every model -- i.e. it must be true in
PLN, classical logic and Bayesian probability.

--linas


>
> I recall that the probabilistic interpretation of
>
> Equivalence (stv 1 1) A B
>
> is
>
> P(A inter B|A union B)
>
> It is explained here but unfortunately the wiki can't render it
>
> http://wiki.opencog.org/w/ExtensionalSimilarityLink
>
> Nil
>
> -------
>> But whatever. All I am saying is that we should allow the following form:
>>
>> EquivalenceScope (stv 1 1)
>>    <empty vardecl>
>>    P
>>    Q
>>
>>   That's all, nothing more.
>>
>> --linas
>>
>>
>>     Nil
>>
>>
>>         --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> <mailto:linasveps...@gmail.com
>>         <mailto:linasveps...@gmail.com>>
>>                  <mailto:linasveps...@gmail.com
>>         <mailto:linasveps...@gmail.com> <mailto: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>
>>         <mailto:b...@goertzel.org <mailto:b...@goertzel.org>>
>>                       <mailto:b...@goertzel.org <mailto:b...@goertzel.org>
>>         <mailto: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>
>>                  <https://www.academia.edu/1016959/Fuzzy_mereology
>>         <https://www.academia.edu/1016959/Fuzzy_mereology>>
>>                       <https://www.academia.edu/1016959/Fuzzy_mereology
>>         <https://www.academia.edu/1016959/Fuzzy_mereology>
>>                  <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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>>                       --
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>>         http://goertzel.org
>>
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