ONT Re: Zeroth Order Theories (ZOT's)
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Turing automata, finitely approximated or not, make my head spin and
my tape go loopy, and I still believe 'twere a far better thing I do
if I work up to that level of complexity in a more gracile graduated
manner. So let us return to our Example in this gradual progress to
that vastly more well-guarded grail of our long-term pilgrim's quest:
| boy male girl female
| o---o child o---o child
| male female \ / \ / child human
| o---o o o o--o
| \ / | | |
| @ @ @ @
|
| (male , female)((boy , male child))((girl , female child))(child (human))
One section of the Theme One program has a suite of utilities that fall
under the title "Theme One Study" ("To Study", or just "TOS" for short).
To Study is to read and to parse a so-called and a generally so-suffixed
"log" file, and then to conjoin what is called a "query", which is really
just an additional propositional expression that imposes a further logical
constraint on the input expression.
The Figure roughly sketches the conjuncts of the graph-theoretic
data structure that the parser would commit to memory on reading
the appropriate log file that contains the text along the bottom.
I will now explain the various sorts of things that the TOS utility
can do with the log file that describes the universe of discourse in
our present Example.
Theme One Study is built around a suite of four successive generators
of "normal forms" for propositional expressions, just to use that term
in a very approximate way. The functions that compute these normal forms
are called "Model", "Tenor", "Canon", and "Sense", and so we may refer to
to their text-style outputs as the "mod", "ten", "can", and "sen" files.
Though it could be any propositional expression on the same vocabulary
$A$ = {"boy", "child", "female", "girl", "human", "male"}, more usually
the query is a simple conjunction of one or more positive features that
we want to focus on or perhaps to filter out of the logical model space.
On our first run through this Example, we take the log file proposition
as it is, with no extra riders.
| Procedural Note. TO Study Model displays a running tab of how much
| free memory space it has left. On some of the harder problems that
| you may think of to give it, Model may run out of free memory and
| terminate, abnormally exiting Theme One. Sometimes it helps to:
|
| 1. Rephrase the problem in logically equivalent
| but rhetorically increasedly felicitous ways.
|
| 2. Think of additional facts that are taken for granted but not
| made explicit and that cannot be logically inferred by Model.
After Model has finished, it is ready to write out its mod file,
which you may choose to show on the screen or save to a named file.
Mod files are usually too long to see (or to care to see) all at once
on the screen, so it is very often best to save them for later replay.
In our Example the Model function yields a mod file that looks like so:
Model Output and
Mod File Example
o-------------------o
| male |
| female - | 1
| (female ) |
| girl - | 2
| (girl ) |
| child |
| boy |
| human * | 3 *
| (human ) - | 4
| (boy ) - | 5
| (child ) |
| boy - | 6
| (boy ) * | 7 *
| (male ) |
| female |
| boy - | 8
| (boy ) |
| child |
| girl |
| human * | 9 *
| (human ) - | 10
| (girl ) - | 11
| (child ) |
| girl - | 12
| (girl ) * | 13 *
| (female ) - | 14
o-------------------o
Counting the stars "*" that indicate true interpretations
and the bars "-" that indicate false interpretations of
the input formula, we can see that the Model function,
out of the 64 possible interpretations, has actually
gone through the work of making just 14 evaluations,
all in order to find the 4 models that are allowed
by the input definitions.
To be clear about what this output means, the starred paths
indicate all of the complete specifications of objects in the
universe of discourse, that is, all of the consistent feature
conjunctions of maximum length, as permitted by the definitions
that are given in the log file.
Have to break here ...
Jon Awbrey
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