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

[Duane Nickull <dnickull@xxxxxxxxx>]

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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