Re: [ontolog-forum] Universal Basic Semantic Structures

[Chris Menzel <chris.menzel@xxxxxxxxx>]

On Sat, Sep 29, 2012 at 2:08 PM, Avril Styrman <Avril.Styrman@xxxxxxxxxxx> wrote:

> ...

> But the isIn or elementOf operator always treats the second operand
> as abstract.  Even if the first operand is a set, the second belongs
> to the category 'set of sets'.  That formalism does not have a simple
> mapping to natural languages, in which plurals do not change category.

Thanks for the summary for my part also. I have only one thing to add.
If we consider only sets with rank 1, that is, no inner sets, then
mereology and set theory become identical.

That's a pretty misleading way to put it as the membership relation in set theory does not correspond to anything in mereology, so there will be many truths of set theory that don't correspond to anything in mereology, e.g., "a ∈ {a}", "a ≠ {a}", etc.

 

Parts and subsets work
identically: you can talk about the set {a,b,c} as well as about the
aggregate abc.

Only for atomic mereologies. Nonatomic mereologies have to be modeled by algebras that are more complex than the powerset algebra.

-chris

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