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Re: [ontolog-forum] Binary versus N-ary relations

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Chris Menzel <chris.menzel@xxxxxxxxx>
Date: Fri, 7 Sep 2012 13:52:58 -0500
Message-id: <CAO_JD6MJ708AhMH8nHk3S4ynVCJcP4mkN1z3MhKu2XZy+OZnQA@xxxxxxxxxxxxxx>
On Fri, Sep 7, 2012 at 11:00 AM, doug foxvog <doug@xxxxxxxxxx> wrote:
On Thu, September 6, 2012 15:44, Andries van Renssen wrote:
> Doug,
> Your statement that occurrences cannot be higher arity relations, because
> they are first class objects implies that you see an opposition between
> 'first class' objects and occurrences.
> I don't know what 'first class objects' are, and I don't see why higher
> arity relations cannot be first class objects.

I guess we have different understanding of what is meant by "relation".
I was taking you to be using two definitions (as many in this forum do):
* A predicate or function, which when applied to a set of values returns
  a truth value.
* A logical statement made using such a predicate/truth function.
To make the distinction, i'll call the second meaning a relation instance.

I find that confusing. Instances of relations are usually understood to be things in the world, actual real world connections like an instance of marriage or paternity between two specific individuals, not linguistic entities. Why not just stick with something like "relational statement" or "atomic statement" or some other piece of more or less conventional terminology?
I agree that an ontology can treat anything it desires as a "first class
object" -- something that it can make statements about by including
it as an argument to a predicate or function.

Those two aren't the same, if by "first-class object" you mean (as I think it usually means) something that is in the range of the individual variables of the language. You can make statements about relations in higher-order logics, but the universe is still falls into into a hierarchy of individuals ("first-class objects"), properties of/relations on individuals, properties of/relations on lower typed entities, etc.
My objection to equating occurrences to relation instances is that
i take the meaning of a relation instance to be fully implied by the
relation itself plus its arguments.  I take any statement about an
actual occurrence to, in the vast majority of cases, only partially
describe the occurrence.  Many additional statements may be made
about the same occurrence -- statements that are not implied by
the first statement.

Very much unlike most of the things you say, I can't make any sense of this at all.


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