ONT Re: Zeroth Order Theories (ZOT's)
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Example. Jets & Sharks
The propositional calculus based on the boundary operator, that is,
the multigrade logical connective of the form "( , , , ... )" can be
interpreted in a way that resembles the logic of activation states and
competition constraints in certain neural network models. One way to do
this is by interpreting the blank or unmarked state as the resting state
of a neural pool, the bound or marked state as its activated state, and
by representing a mutually inhibitory pool of neurons p, q, r by means
of the expression "( p , q , r )". To illustrate this possibility,
I transcribe into cactus language expressions a notorious example
from the "parallel distributed processing" (PDP) paradigm [McR]
and work through two of the associated exercises as portrayed
in this format.
Logical Input File: JAS = ZOT(Jets And Sharks)
o----------------------------------------------------------------o
| |
| (( art ),( al ),( sam ),( clyde ),( mike ), |
| ( jim ),( greg ),( john ),( doug ),( lance ), |
| ( george ),( pete ),( fred ),( gene ),( ralph ), |
| ( phil ),( ike ),( nick ),( don ),( ned ),( karl ), |
| ( ken ),( earl ),( rick ),( ol ),( neal ),( dave )) |
| |
| ( jets , sharks ) |
| |
| ( jets , |
| ( art ),( al ),( sam ),( clyde ),( mike ), |
| ( jim ),( greg ),( john ),( doug ),( lance ), |
| ( george ),( pete ),( fred ),( gene ),( ralph )) |
| |
| ( sharks , |
| ( phil ),( ike ),( nick ),( don ),( ned ),( karl ), |
| ( ken ),( earl ),( rick ),( ol ),( neal ),( dave )) |
| |
| (( 20's ),( 30's ),( 40's )) |
| |
| ( 20's , |
| ( sam ),( jim ),( greg ),( john ),( lance ), |
| ( george ),( pete ),( fred ),( gene ),( ken )) |
| |
| ( 30's , |
| ( al ),( mike ),( doug ),( ralph ), |
| ( phil ),( ike ),( nick ),( don ), |
| ( ned ),( rick ),( ol ),( neal ),( dave )) |
| |
| ( 40's , |
| ( art ),( clyde ),( karl ),( earl )) |
| |
| (( junior_high ),( high_school ),( college )) |
| |
| ( junior_high , |
| ( art ),( al ),( clyde ),( mike ),( jim ), |
| ( john ),( lance ),( george ),( ralph ),( ike )) |
| |
| ( high_school , |
| ( greg ),( doug ),( pete ),( fred ),( nick ), |
| ( karl ),( ken ),( earl ),( rick ),( neal ),( dave )) |
| |
| ( college , |
| ( sam ),( gene ),( phil ),( don ),( ned ),( ol )) |
| |
| (( single ),( married ),( divorced )) |
| |
| ( single , |
| ( art ),( sam ),( clyde ),( mike ), |
| ( doug ),( pete ),( fred ),( gene ), |
| ( ralph ),( ike ),( nick ),( ken ),( neal )) |
| |
| ( married , |
| ( al ),( greg ),( john ),( lance ),( phil ), |
| ( don ),( ned ),( karl ),( earl ),( ol )) |
| |
| ( divorced , |
| ( jim ),( george ),( rick ),( dave )) |
| |
| (( bookie ),( burglar ),( pusher )) |
| |
| ( bookie , |
| ( sam ),( clyde ),( mike ),( doug ), |
| ( pete ),( ike ),( ned ),( karl ),( neal )) |
| |
| ( burglar , |
| ( al ),( jim ),( john ),( lance ), |
| ( george ),( don ),( ken ),( earl ),( rick )) |
| |
| ( pusher , |
| ( art ),( greg ),( fred ),( gene ), |
| ( ralph ),( phil ),( nick ),( ol ),( dave )) |
| |
o----------------------------------------------------------------o
We now apply Study to the proposition that
defines the Jets and Sharks knowledge base,
that is to say, the knowledge that we are
given about the Jets and Sharks, not the
knowledge that the Jets and Sharks have.
With a query on the name "ken" we obtain the following
output, giving all of the features associated with Ken:
Sense Outline: JAS & Ken
o---------------------------------------o
| ken |
| sharks |
| 20's |
| high_school |
| single |
| burglar |
o---------------------------------------o
With a query on the two features "college" and "sharks"
we obtain the following outline of all of the features
that satisfy these constraints:
Sense Outline: JAS & College & Sharks
o---------------------------------------o
| college |
| sharks |
| 30's |
| married |
| bookie |
| ned |
| burglar |
| don |
| pusher |
| phil |
| ol |
o---------------------------------------o
From this we discover that all college Sharks
are 30-something and married. Furthermore,
we have a complete listing of their names
broken down by occupation, as I have no
doubt that all of them will be in time.
| Reference:
|
| McClelland, James L. & Rumelhart, David E.,
|'Explorations in Parallel Distributed Processing:
| A Handbook of Models, Programs, and Exercises',
| MIT Press, Cambridge, MA, 1988.
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