Hi folks, (01)
n my understanding of categories (semantic primitives), besides objects,
properties and relations there are twin concepts that are the subject of
Basics: a concept in semantic transformation is a form and and a content at
the same time, which is flip-flopped. The form of a concept is the name
(word, or words) and the content is what you "know" about a chunk of reality
marked by that concept (form)
Since we all have different experience of different chunks of reality, we
need to harmonize our understanding of the world and that is done by
semantic parsing. The result of any effort to make sense of the world
depends on the condition whether you see the whole picture (an integer) or
just a part. Anything seen as a whole (pattern, form) is understood, parts
are not. So in learning about the world you always isolate a whole by
creating another whole ad infinitum. That is done by controling the distance
between you and your object and changing your focus. What is a whole is
determined by its boundaries. No boundaries, not a whole, but a part, and a
part is beyond us, see merelogy. You should know this thread better than me.
So what you can do in harmonising is to coordinate (in space) and to
synchronize (in time) your experience and vocabulary.
There is no mapping between words of two different languages. What you are
mapping is the reality onto your semantic frames and your output is
knowledge representation which should be semantically parsed to see if you
can relate the chunk of reality to your experience of the same - that may
have a different set of words to describe it.
The ultimate form is a number, and a number is both quality and quantity.
When you look at a number as a form, it has to have content, the entity
that the number identifies.
Most of the mental operations are centered around identification. You
identify the form, but you want to see the content. The same is described in
in detail in information theory.
Now what you want to retrieve in a knowledge representation system must be
marked/made available technically for retrieval before you start searching.
Knowledge is an ordered access to information. Since you identify by form,
that is by number, and repository in alpha sort will never be well
structured or logical for retrieval. Your mind does not work that way
anyway. Besides, the relations must also be represented, but the current
relations used in ontologies are practicaly spatial relations or even worse,
partial, which is a no go anyway. So where are we as far as time is
concerned? Time is not posible to divide into present, past and future,
because of the lack of clear boundaries. You need movement to define time in
relation to space and vice versa. Movement is not to be registered as a
story or or a series of events or states. Movement is your operations, the
movement of the mind through mental steps producing concepts. Concept is a
product, a product of multiplication that need to be broken down into a
sequence of repeated additions or cycles. Otherwise you cannot perform this
mental operation. (Every entiy has a boudary in the world its date of
conception and death and the same is true of concepts created, regardless of
whether you use that or are aware of that at all.) The computer cannot
either. Why? Because of the management of time and space. If you cannot
follow me, pop me a question. Regards
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> Sent: 31 January 2009 04:19
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Ontology and Category Theory
> On Jan 30, 2009, at 3:56 PM, Len Yabloko wrote:
> > Mitch,
> >> On Fri, Jan 30, 2009 at 12:36 PM, Len Yabloko <lenya@xxxxxxxxxxxxx>
> >> wrote:
> >>> my impression of CT remains to be as of an attempt to make
> >>> abstract reasoning in general (not only mathematical form of it)
> >>> more precise.
> >> If anything, the executive summaries of logic and category theory
> >> are:
> >> logic is the study of reasoning.
> >> category theory is the study of transformations.
> > Reasoning and transformations are closely related to each other,
> > even in strict mathematical sense- I believe.
> Its hard to say whether this is true or not until you say what you
> mean more precisely what you mean. There are certainly connections
> between logics and CT, which is hardly surprising given that CT is
> such a very general theory. One connection is that formal reasoning
> systems - more exactly, formal proof systems - form a natural category
> in which the sentences are the objects and the proofs are the
> morphisms: a proof with A as premis and B as conclusion is the
> 'mapping' from A to B. (Exercise for the reader: show that this is a
> category. You have to show that the morphism composition is
> associative and that there is an identity morphism. Hint: its so
> simple you might find it hard to see that there is anything to do.)
> So that is one relationship between reasoning and transformations,
> yes. Is that the one you had in mind?
> >> Sure a gross oversimplification, but I think in the appropriate
> >> direction for each, and it allows meaningful distinction and
> >> comparison. It might be difficult to extract the above from wikipedia
> >> or other easy online sources, but still it's a start.
> > It is not that difficult to extract since 'morphisms' are at the
> > very definition of Category. What is difficult is to understand what
> > it is 'appropriate direction' for each. I dawned on me long time ago
> > that both complement each other
> Can you elaborate on this insight? In what sense do they complement
> each other?
> > , but I still can't figure out why everybody insists on keeping them
> > separate (and seemingly as far from each other as possible).
> They clearly are separate. They are different topics, with different
> motivations and different methods and topics of interest. It isn't at
> all remarkable that they are separate. They do have connections, cf.
> the above, which have of course been thoroughly explored.
> > What am I missing?
> >>> I believe this objective to be a paramount to making it useful
> >>> beyond calculation and in the real of reasoning. If I am wrong and
> >>> CT is not attempting to do that, then some other theory should.
> >>> And my observation is that neither classical Logic nor Ontology as
> >>> discipline are adequate to this goal if they can't "nail down' the
> >>> identity.
> >> There's all sorts of discussion within the ontology community about
> >> identity. Whether the unique name assumption (UNA) holds, inferring
> >> subsumption of one concept by another.
> >>> Again, I not talking about absolute and universal identity (I
> >>> don't know what it is), but about sufficient level of
> >>> identification required for business transactions.
> >> If you're concerned that a particular formalism might be
> >> inappropriate
> >> for business transactions, then CT is definitely it. Even
> >> well-educated and, separately, intelligent people have difficulties
> >> with even boolean logic.
> > I always thought that you don't need to be a specialist to apply
> > someone else specialty to your work. Isn't it the job of specialist
> > to make it possible?
> No. The job of the specialist is to specialize. :-)
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