ONT Re: Zeroth Order Theories (ZOT's)
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The last two functions in the Study section, "Canon" and "Sense",
extract further derivatives of the normal forms that are produced
by Model and Tenor. Both of these functions take the set of model
paths and simply throw away the negative labels. You may think of
these as the "rose colored glasses" or "job interview" normal forms,
in that they try to say everything that's true, so long as it can be
expressed in positive terms. Generally, this would mean losing a lot
of information, and the result could no longer be expected to have the
property of remaining logically equivalent to the original proposition.
Fortunately, however, it seems that this type of positive projection of
the whole truth is just what is possible, most needed, and most clear in
many of the "natural" examples, that is, in examples that arise from the
domains of natural language and natural conceptual kinds. In these cases,
where most of the logical features are redundantly coded, for example, in
the way that "adult" = "not child" and "child" = "not adult", the positive
feature bearing redacts are often sufficiently expressive all by themselves.
Canon merely censors its printing of the negative labels as it traverses the
model tree. This leaves the positive labels in their original columns of the
outline form, giving it a slightly skewed appearance. This can be misleading
unless you already know what you are looking for. However, this Canon format
is computationally quick, and frequently suffices, especially if you already
have a likely clue about what to expect in the way of a question's outcome.
In the present Example the Canon function
generates a Can file that looks like this:
Canon Output and
Can File Example
o-------------------o
| male |
| child |
| boy |
| human |
| female |
| child |
| girl |
| human |
o-------------------o
The Sense function does the extra work that is required
to place the positive labels of the model tree at their
proper level in the outline.
In the present Example the Sense function
generates a Sen file that looks like this:
Sense Output and
Sen File Example
o-------------------o
| male |
| child |
| boy |
| human |
| female |
| child |
| girl |
| human |
o-------------------o
The Canon and Sense outlines for this Example illustrate a certain
type of general circumstance that needs to be noted at this point.
Recall the model paths or the feature specifications that were
numbered <2> and <4> in the listing of the output for Tenor.
These paths, in effect, reflected Model's discovery that
the venn diagram cells for male or female non-children
and male or female non-humans were not excluded by
the definitions thare were given in the Log file.
In the abstracts given by Canon and Sense, the
specifications <2> and <4> have been subsumed,
or absorbed unmarked, under the general topics
of their respective genders, male or female.
This happens because no purely positive
features were supplied to distinguish
the non-child and non-human cases.
That completes the discussion of
this six-dimensional Example.
Nota Bene, for possible future use. In the larger current of work
with respect to which this meander of a conduit was initially both
diversionary and tributary, before those high and dry regensquirm
years when it turned into an intellectual interglacial oxbow lake,
I once had in mind a scape in which expressions in a definitional
lattice were ordered according to their simplicity on some scale
or another, and in this setting the word "sense" was actually an
acronym for "semantically equivalent next-simplest expression".
Jon Awbrey
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