SUO: Re: Critique Of Non-Functional Reason
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| A. Automated Reasoning (AR)
|
| The standard will be suitable for automated logical inference
| to support knowledge-based reasoning applications.
|
| B. Inter-Operability (IO)
|
| The standard will provide a basis for achieving Inter-Operability
| among various software and database applications.
[AB]
Let's say that have taken up a dual object pair (R^k, R^k -> R).
We think of the space R^k as representing the "geometric" aspect
of the situation, where the various subsets U c R^k are like so
many geometric figures and bodies in the space of choice, while
the function space (R^k -> R) represents the "functional" aspect
of the situation, with the various functions f : R^k -> R being
like "fields of intensity" or "indices of classification" that
organize or valuate the points of the underlying space R^k.
Now, just because we are using a particular space R as a basis
for coding entities of interest to us does not mean that we are
really using all of the properties of that space, or would even
care to do so. It is entirely possible that we are making use
of R in a less rigid, more topologically flexible fashion, and
even employing the functional values in R in ways that are not
to be taken literally. People sometimes distinguish different
levels of "scales", such as "ratio", "interval", "categorical",
and "nominal", but the room for variation is endless here.
At one extreme end on this "scale of scales", we might as well
be talking about a dual pair (B^k, B^k -> B), where B = {0, 1},
for all the fineness of discrimination that we need to maintain
in each space. This is called the dual pair of boolean spaces
and functions, alias "colorings of the k-cube", "truth tables",
or "venn diagram world". And here we can approach the level
courses of zeroth order logic in a purely functional vein.
Jon Awbrey
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