Dear Duane,
That looks fine. There will be an elegant way to say that in
Common Logic (KIF is dead long live CL). I will defer to Chris M on what that
is.
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 17:32
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
Matthew/John
Thank you. This speaks to me as a developer.
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? For example, please see the attached diagram to tell me if it
makes sense. 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?
Duane
On 2/4/10 5:17 AM, "John F. Sowa" <sowa@xxxxxxxxxxx>
wrote:
Dear Matthew and Duane,
MW> It is the most basic thing about sets that they are defined
> by their membership, which does not change.
Yes. If you write something like the following,
S1 = S union {x}
mathematicians don't say that S has changed, but that S1 is
a different set.
In programming languages, it is common to write
x = x + 1;
but when that operation is carefully analyzed and described,
it's described as "the value stored at the location designated
by x has been replaced or updated with a new value."
There are also some programming languages, such as ML or Haskell,
called *functional* or *single-assignment* languages in which
no variable can be reassigned a different value -- i.e., no
statement of the form x=x+1 is permitted.
MW> 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.
The usual distinction:
The identity conditions for a set are *extensional*: if
S1 and S2
have the same members, they are identical; otherwise they are
two
different sets.
The identity conditions for a type are *intensional*; two
types
T1 and T2 are identical if their definitions are equivalent;
their set of instances in a particular world w is called
their
*denotation* in w. Those worlds may be, for example,
the physical
world or a particular computer system at different times.
John
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