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

[Duane Nickull <dnickull@xxxxxxxxx>]

Pat:

Thank you.  This is very clear and easy to understand.  

Duane

On 2/4/10 10:08 PM, "Pat Hayes" <phayes@xxxxxxx> wrote:

> 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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---
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