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

To: Duane Nickull <dnickull@xxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 5 Feb 2010 00:08:18 -0600
Message-id: <D9040BCB-ED7A-49BE-A5C5-5BF1F6232C85@xxxxxxx>
Let me try, Duane.

On Feb 4, 2010, at 12:37 AM, Duane Nickull wrote:

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?

A set is defined as a collection of things, in an abstract sense of 'collection'. It is defined by its members or elements: if A has the same members as B, and A and B are sets then A *is* B. There isn't anything to a set other than the members it has; it has no 'identity' beyond being the set of things that it is a set of.  A set is not a separate 'thing' with a state that can be updated or changed. It is not a data structure. So, to answer your questions: no, a set cannot add new members. First, the idea of a set doing anything (like 'adding" ) doesn't make sense; but even if it did, adding something to a set makes a new set, one that is different from the first set. Sets cannot change their lists (they don't have lists, anyway) and members cannot be retracted: if you 'take something out of' a set, then you have a different set. 

Make sense?

Pat H.


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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