Re: Topic :> Dynamics Of Ontologies

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Topic :> Dynamics Of Ontologies 17

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Example 1.  Prognostic Signs And Symptoms (cont.)

A very common event in the life of inquiry has just occurred:
we have made a mistake -- who's "we", you say? -- okay, then,
I made a mistake.  The error would most likely come to light
if and when I try to use my Initial Theory for some critical
purpose under heaven, and almost certainly if I were to test
the logical consequences of its presumptive truth within the
deductive closure of Plato's heaven.  There are at least two
ways that this mistake could have occurred.  First of all, I
may not understand the full logical meaning of the statement
that I have written down as my Initial Theory.  For instance,
I may believe that it has some meaning that it does not have,
often on account of some tacit assumption that I think to be
in force, when in fact I haven't written this assumption out.
More simply, it may happen that I know the meaning of what I
have written, but have written a theory that is not the case.

Not being able to read my mind, all that an outside observer
can do is to examine whether my theory accords with the data
that was given.  One of the best ways to do this, if matters
are simple enough to allow it, is to detail as completely as
possible the empirical coverage of the theory in view.  What
makes this feasible at all is that we do not have to examine
all of the things in all of the worlds that the theory might
cover, its so-called "models", but only the models in so far
as they are describable in the terms of the given vocabulary.
This allows us to shift our attention from models that exist
in reality, in the real world, so to speak, to formal models,
those that can be said to exist only in the sense that their
descriptions are logically consistent.  This tactic lightens
the workload considerably, but the downside is that it leads
many to confuse the things described with their descriptions.
Indeed, it has been known to happen that people of a certain
bent may focus so exclusively on the formal models that they
almost appear to forget about the existence of the real ones.

Remark.  In this discussion we have used the term "model" as
a shorthand way of talking about a set of basic descriptions
of logical models.  The next time I go over this terrain, in
order to avoid the types of sign-object confusions mentioned
above, I'm thinking about trying the word "manifest" instead.

The link between a Theory and its Model Set, or its Manifest,
can be cast by way of the kind of exact logical relationship
that C.S. Peirce referred to as "deductive" or "explicative".
I'll discuss this in detail later on, but for now let's just
look at the output of an algorithm that generates the models
of propositional formulas, as applied to our Initial Theory.
The result, loosely referred to as the Initial Model (Set),
is shown in the following display that attaches to Node 3.

Node 3.  Initial Model -- http://suo.ieee.org/ontology/gif00006.gif

o-----------------------------------------------------------o
| Node 3.  Initial Model                                    |
o-----------------------------------------------------------o
|                                                           |
|   delirium                                                |
|    laughter                                               |
|     seriousness                                           |
|      less_dangerous                                       |
|       more_dangerous *                                    |
|       (more_dangerous ) -                                 |
|      (less_dangerous ) -                                  |
|     (seriousness )                                        |
|      less_dangerous *                                     |
|      (less_dangerous ) -                                  |
|    (laughter )                                            |
|     seriousness                                           |
|      more_dangerous *                                     |
|      (more_dangerous ) -                                  |
|     (seriousness ) *                                      |
|   (delirium ) *                                           |
|                                                           |
o-----------------------------------------------------------o

This output says that models with the following conjunctions of
positive and negative features are allowed by the Initial Theory:

1.   delirium  laughter  seriousness  less_dangerous  more_dangerous
2.   delirium  laughter (seriousness) less_dangerous
3.   delirium (laughter) seriousness  more_dangerous
4.   delirium (laughter)(seriousness)
5.  (delirium)

In this summary, any logical feature that does not appear in
a conjunctive list may be assumed to vary freely through its
positive and negative conditions, independently of the rest.

This amounts to a lot more models than I really intended,
and the reason for the over-generation is evidently that
I placed no explicit constraints on the co-occurrence of
logical features within the pairs {laughter, seriousness}
and {less_dangerous, more_dangerous}, which were tacitly
taken for granted as dichotomous pairs of properties.

But tacit measures rule out nothing in logical scores.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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