ONT Re: Zeroth Order Theories (ZOT's)

[Jon Awbrey <jawbrey@oakland.edu>]

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

We are considering an Example of a propositional expression
that is formed on the following "alphabet" or "lexicon" of
six "logical features" or "boolean variables":

$A$  =  {"boy", "child", "female", "girl", "human", "male"}.

The expression is this:

|   ( male  , female )
|   (( boy  , male child ))
|   (( girl , female child ))
|   ( child ( human ))

Putting it very roughly -- and putting off a better description
of it till later -- we may think of this expression as notation
for a boolean function f : %B%^6 -> %B%.  This is what we might
call the "abstract type" of the function, but we will also find
it convenient on many occasions to represent the points of this
particular copy of the space %B%^6 in terms of the positive and
negative versions of the features from $A$ that serve to encase
them as logical "cells", as they are called in the venn diagram
picture of the corresponding universe of discourse X = [$A$].

Just for concreteness, this form of representation begins and ends:

<0,0,0,0,0,0>  =  (boy)(child)(female)(girl)(human)(male),
<0,0,0,0,0,1>  =  (boy)(child)(female)(girl)(human) male ,
<0,0,0,0,1,0>  =  (boy)(child)(female)(girl) human (male),
<0,0,0,0,1,1>  =  (boy)(child)(female)(girl) human  male ,
...
<1,1,1,1,0,0>  =   boy  child  female  girl (human)(male),
<1,1,1,1,0,1>  =   boy  child  female  girl (human) male ,
<1,1,1,1,1,0>  =   boy  child  female  girl  human (male),
<1,1,1,1,1,1>  =   boy  child  female  girl  human  male .

And I'm sure that you can guess what you'll find in Middle Earth.

Have to break here ...

Jon Awbrey

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤