[Inquiry] Re: Differential Logic -- Series B
Jon Awbrey
jawbrey at att.net
Fri Feb 20 12:02:13 CST 2004
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DLOG. Note B10
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Sub*Title. There's Gonna Be A Rumble Tonight!
From: "Theme One: A Program of Inquiry",
Jon Awbrey & Susan Awbrey, August 9, 1989.
Example 5. Jets and Sharks
The propositional calculus based on the boundary operator
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 A, B, C
in the expression "(A, B, C)". To illustrate this possibility,
we transcribe a well-known example from the parallel distributed
processing literature [McR] and work through two of the associated
exercises as portrayed in Existential Graph format.
File "jas.log". Jets and Sharks Example
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
defining the Jets and Sharks data base.
With a query on the name "ken" we obtain the following
output, giving all the features associated with Ken:
File "ken.sen". Output of Query on "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 features satisfying these constraints:
File "cos.sen". Output of Query on "college" and "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.
Further, we have a complete listing of their names broken down by occupation,
as no doubt all of them will be, eventually.
Reference.
| McClelland, James L. & Rumelhart, David E.,
|'Explorations in Parallel Distributed Processing:
| A Handbook of Models, Programs, and Exercises',
| MIT Press, Cambridge, MA, 1988.
Those who already know the tune,
Be at liberty to sing out of it.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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