Thank you, Pat.
The core message was that the "class membership relation is not transitive"
unlike the class inclusion relation.
Azamat
----- Original Message -----
From: "Pat Hayes" <phayes@xxxxxxx>
To: "AzamatAbdoullaev" <abdoul@xxxxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Monday, September 05, 2011 6:41 AM
Subject: Re: [ontolog-forum] Universal and categories in BFO & DOLCE (01)
Just a quick correction of a misleading error: (02)
On Sep 4, 2011, at 2:18 PM, AzamatAbdoullaev wrote: (03)
> On Sunday, September 04, 2011 1:48 PM, Pat Browne wrote:
...
> "Question 2: In DOLCE could it be the case a particular could be an
> element of a universal and an element of a category as follows: ((P
> isElementOf U) and (U isSubsetOf C) => (P isElementOf C) = true)."
>
> That's another misconception.
> In fact, ((P isElementOf U) and (U isSubsetOf C) => (P isElementOf C) =
> false)."
> You may discard the ontologies which are missing to formulate that "the
> class membership relationship is not transitive, while the class inclusion
> is transitive."
> Here is a staple example: "An individual human is a member of the class of
> humans. The class of humans is a member of the class of species of
> animals.
> But a human being is not a member of the class of species." (04)
This is not a counterexample. This has the pattern ((P element of U) & (U
element of Z)) => P element of Z), which indeed is not a valid inference.
But this is a different inference than the one being discussed, since member
and Subset are not the same notion. (05)
Pat Hayes (06)
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