Doug, (01)
I like your rationale about naming the nodes specific to an ontological
domain, so yes, T and UnT work if the ontology is about lattices, but not if
the ontology is about linear discrete time systems. (02)
But it would still be nice if everyone would use the symbols I like for the
GUT and LLT nodes of the lattice. (03)
JMHO,
-Rich (04)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (05)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of doug foxvog
Sent: Friday, August 20, 2010 2:23 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Triadic Sign Relations (06)
On Thu, August 19, 2010 15:40, Schiffel, Jeffrey A said:
> Hi, Rich,
>
> I like the use of 'T' because of its association with lattices, and
> therefore with ontologies. (07)
The symbol "T", to me, means "true" and is used as such in various logics
and computer programs. It does not suggest to me the set or class of
everything. "T" also has other meanings in other scientific and
engineering domains. Since terms in ontologies generally use terms from
the domains of discussion, selection of such a name, not from the domain
which the ontology is about, strikes me as a poor choice. (08)
The name of this class in a given ontology does not matter to
me, although "Everything" or "Anything" both strike my fancy. I have no
complaint with the term "Thing", which is used in various major ontologies,
but recognize that some people like to reserve the term for physical
objects. The use of a full URL or namespace designation (e.g., cyc:Thing)
would be sufficient to make the meaning clear to anyone who can then look
up the definition of the term. (09)
> If s is the largest element smaller than (or equal to) both x and y (010)
I suppose "smaller than" and "largest" are related to position in a
partial ordering. E.g., a set would only be "smaller than" its supersets,
and a larger (finite) set would have more elements than a smaller one. (011)
> and s
> is greater than (or equal to) t, then it is the greatest lower bound of x
> and y. It is called the infimum. Similarly, if s is the smallest element
> greater than (or equal to) both x and y, and s is less than or equal to,
> then it is the least upper bound. Call the greatest lower bound the
> infimum and the least upper bound the supremum of the pair x and y. Then a
> lattice is a partially ordered set (U, 'less than or equal') in which
> every pair of elements (x, y) in U has a sup and an inf in U.
>
> Lattices are the basis for many ontologies. A common notation for the top
> supremum of the entire lattice is T. The lowest infimum is then notated as
> an inverted T. (This, incidently, is the notation used in formal concept
> analysis.
>
> So I like T, but your exception is noted. (012)
If we were discussing an ontology of latices, i would like the term "T",
too. But we are not. (013)
-- doug foxvog
>
> Regards,
>
> -- Jeff Schiffel
>
> ________________________________
>
> Rich Cooper wrote,
>
> Hi John,
>
>
>
> I kinda object to the use of "T" because it conflicts with the extremely
> long history of dynamic systems, discrete time systems, even electronics
> which is often spread out in a frequency v time plane. Wavelets, Fourier
> analysis, control systems, optimal controls, discrete sampled systems, and
> zillions of other engineering marvels use "T" and have for centuries. It
> seems unnecessary to displace it now.
>
>
>
> < snippage >
>
>
>
> ________________________________
>
> -----Original Message-----
> From: John F. Sowa
>
>
>
> On 8/17/2010 6:29 AM, Rich Cooper wrote:
>
>> I interpret "comprehension" in this passage as referring to the degree
>
>> of specialization of a "term", or symbol.
>
>
>
> < snip >
>
>
>
> I'd also like to relate this discussion to the term used for the
>
> top of a type hierarchy. My preferred term is the symbol T for top,
>
> because it avoids all possible confusion with words like 'thing'
>
> or 'concept'. If anybody wants a pronounceable word, I recommend
>
> 'entity' because it is a technical term that avoids all kinds of
>
> pointless controversy about whether an event or a property is a thing.
>
>
>
> The crucial point about T (or whatever else you want to call it) is
>
> that it has maximum extension: The corresponding predicate T(x)
>
> is true of every and any x that anybody can imagine. There is
>
> one and only one axiom that defines the predicate T(x):
>
>
>
> For every x, T(x).
>
>
>
> But T also has the minimum possible comprehension (or intension):
>
> zero. That single axiom, which is true of everything, says nothing
>
> about anything. T has no attributes or properties of any kind.
>
>
>
> > I interpret "comprehension" in this passage as referring to the
>
> > degree of specialization of a "term", or symbol.
>
>
>
> It's better not to try to explain it. Just think in terms of
>
> the logic: The comprehension (or intension) is determined by
>
> the differentiae (monadic predicates) that define it: adding
>
> more differentiae makes a term more specialized, and deleting
>
> differentiae makes it more generalized. If you erase all the
>
> differentiae, you get T.
>
>
>
> < remainder snipped >
>
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doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (015)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
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