Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

["Matthew West" <dr.matthew.west@xxxxxxxxx>]

Dear Duane,

 

It is the most basic thing about sets that they are defined by their membership, which does not change. So if you have something that has members, but the membership can change, then what you  know for certain is that it is not a set. Some people use the word type for such things. A type will have, at a point in time, a set which is its membership.

 

One of the attractions to me of 4D with possible worlds is that you do not need types, because 4D essentially makes things timeless and unchanging, and possible worlds allows you  to deal with the intentional.

 

Interestingly here it is membership that is the root primitive, rather than set or type. Sets have an axiom that says that if two sets have the same membership they are the same set, whereas types do not have that axiom.

 

Regards

 

Matthew West                           

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From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Duane Nickull
Sent: 04 February 2010 06:37
To: doug@xxxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

 

Doug:

Can you please clarify what you mean by “Sets are timeless; they cannot change their members”. Do you mean they cannot add new members?  Can they not change enumeration lists of existing members?  Can existing members values be retracted?

D


On 2/3/10 5:47 PM, "doug  foxvog" <doug@xxxxxxxxxx> wrote:

The definition should start out that a set has members.  Restrictions
on the permissible types of members can identify different types of set,
or in given contexts may limit what is considered to be a generic set.
Sets are timeless; they cannot change members.  If an element which is not
in a set is added to a set, the result is a different set.

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