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

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Thu, 4 Feb 2010 12:08:13 -0600
Message-id: <3243CF6D-C2F5-44D1-80F9-91B60D2AAD16@xxxxxxxx>
On Feb 4, 2010, at 11:32 AM, Duane Nickull wrote:
> ...I remember writing equations using the membership operator (the one that 
>looks like a rounded “E”).  Is this symbol representative of the same type 
>of membership?    (01)

∈ is the usual symbol for membership in set theory.    (02)

> For example, please see the attached diagram to tell me if it makes sense.    (03)

PNG image

That works fine as long as you've defined ⊕ explicitly as exclusive 
disjunction:    (01)

   p ⊕ q =def (p ∨ q) ∧ ¬(p ∧ q)    (02)

In case anyone's mailer doesn't do unicode:    (03)

Attachment: latex-image-1.pdf
Description: Adobe PDF document

> I tried to express that x is a member of either P or S but cannot be a 
>member of both.  Is there a better way to write this in KIF?    (01)

Better?  No, it's an just alternative way to write things in first-order logic. 
 In KIF (better, CLIF, which has superseded KIF) you would just write exactly 
what you just said:    (02)

  (and (or (memberOf x P) (memberOf x S)) 
       (not (and (memberOf x P) (memberOf x S))))    (03)

Alternatively, if you have union and intersection set operators available to 
you:    (04)

  (and (memberOf x (union P S))
       (not (memberOf x (intersection P S))))    (05)

And, of course, you can also define an exclusive disjunction operator "xor" as 
above and then simply write in CLIF what you formalized above:    (06)

  (xor (memberOf x P) (memberOf x S))    (07)

-chris    (08)

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