Re: SUO: RE: Problems in SUMO
Ian --
Many thanks for the correction. I did indeed
misconstrue the meaning of "partition" in SUMO.
It is indeed a partition of instances, not of classes.
I was misled by the documentation of "exhaustiveDecomposition"
and didn't check the axioms thoroughly enough. I should
also have noticed that the Integers had direct subclasses
other than "EvenInteger" and "OddInteger". All the
"partitions" I had looked at had no additional
classes.
Matthew was right. Mea Culpa!
Bottom line: SUMO could add classes at the top
semantic level without changing the "partition"
assertion.
As for whether such additional classes are
actually necessary to allow accurate translation of
SUMO concepts to other ontologies, such as OpenCyc
or DOLCE which have such top-level classes,
this is rather complicated and will have to be
discussed in a separate thread. My suspicion
is that such classes will be needed.
Pat
==================
Ian Niles wrote:
>> >
>> > MW: Maybe we are at cross purposes here at what is possible. Let me
>> > try an example with integers. I can partition the integers into odd
>> > and even numbers. However, this does not prevent me from also
>> > partitioning the integers into prime and non-prime numbers. These
>> > two partitions are orthogonal to each other.
>> >
>>[PC] Yes, "Even" and "Odd" are disjoint classes, and "Prime" and "not
>>prime" are also disjoint classes with a different intentional basis.
>>One can create such disjoint classes, and they can live happily
>>together, *provided* that no two of them are also declared a
>>"partition" on the class of Integers.
>> As I understand it, in SUMO a "partition" declaration on a
>>class "(partition Entity Abstract Physical)" doesn't just mean
>>that Abstract and Physical are disjoint classes, it means that
>>there are not and cannot ever be any other *classes* at the same
>>level as "Abstract" and "Physical").
>
>
[IN]
> No, this is false, but I now see how you came to this interpretation, and I
> bear at least part of the blame.
>
>
>
[PC]>>The definition of partition
>>in SUMO is:
>> > "A &%partition of a class C is a set of mutually &%disjoint
>> > classes (a subclass partition) which covers C. Every instance of C
>> > is an instance of exactly one of the subclasses in the partition."
>> . . . with the axiom:
>> > (<=> (partition @ROW) (and
>> > (exhaustiveDecomposition @ROW)
>> > (disjointDecomposition @ROW)))
>>
>>The definition of an "exhaustiveDecomposition" in SUMO is:
>> > "An &%exhaustiveDecomposition of a &%Class C is a set of subclasses
>> > of C such that every subclass of C either is an element of the set
>> > or is a subclass of an element of the set. Note: this does not
>> > necessarily mean that the elements of the set are disjoint (see
>> > &%partition - a &%partition is a disjoint exhaustive
>> > decomposition.)"
>> . . . with the axiom:
>> > (=> (exhaustiveDecomposition ?CLASS @ROW)
>> > (forall (?OBJ)
>> > (=> (instance ?OBJ ?CLASS)
>> > (exists (?ITEM)
>> > (and (inList ?ITEM (ListFn @ROW))
>> > (instance ?OBJ ?ITEM))))))
>
>
{IN]
> I think the documentation string is confusing here (and I'll revise it).
> What it should say is the following (note that this interpretation is what
> is stated formally by the corresponding axiom):
>
> "An &%exhaustiveDecomposition of a &%Class C is a set of subclasses of C
> such that
> every instance of C is an instance of one of the subclasses of the set.
> Note: this does not
> necessarily mean that the elements of the set are disjoint (see &%partition
> - a &%partition
> is a disjoint exhaustive decomposition)."
>
>
[PC]
>> So, if one were to say in SUMO:
>>
>> (partition Integers EvenNumbers OddNumbers)
>>
>> . . . then one could not create a class of "PrimeNumber" as
>>a direct subclass of "Integer". In fact, in that case
>>"PrimeNumber" would be an incoherent concept, inexpressible
>>in SUMO (since every instance of PrimeNumber would necessarily
>>be an instance of Integer, but no one class could ever contain all
>>the prime numbers). You could create a subclass under "EvenNumber"
>>of "EvenPrimeNumber" and a subclass under "OddNumber" of
>>"OddPrimeNumber" but you couldn't have any one class that
>>included only those two classes, because that combined class would
>>necessarily be a forbidden subclass of "Integer" (it could not
>>be a subclass of either "EvenNumber" or "OddNumber").
>>That's what SUMO "partition" does to a class, and why it needs to be
>>used judiciously. I though that the SUMO usage of "partition"
>>was known to all.
>
>
[IN]
> No, this isn't right. Given the formal axiom for 'exhaustiveDecomposition',
> the statement '(partition Integer EvenNumber OddNumber)' means just the
> following:
>
> 1. Every integer is either odd or even.
>
> 2. There is no number which is both even and odd.
>
> Neither 1 nor 2 prevents one from defining a class, as we do in the SUMO, of
> prime numbers which is a subclass of 'Integer' and which contains both even
> and odd numbers.
>
>
[PC]>> For that reason, declaring a partition on Abstract and Physical
>>would also preclude creating any classes that have instances of
>>"Abstract" as well as instances of "Physical".
>
>
[IN]> No, this is false for the same reason.
>
>
[PC]
>> That is how I interpret the "partition" declaration. In his
>>response, Ian did not contradict this interpretation. Perhaps he
>>has a different interpretation? Have I misconstrued?
>
>
[IN]
> Please let me know if this doesn't clear things up. As I mentioned, the
> documentation string for 'exhaustiveDecomposition' was not adequate.
>
>
Yes, as I review the axioms more carefully, I see now
that they do not support the interpretation I had.
Pat
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