[Inquiry] Re: Differential Logic -- Series B

[Jon Awbrey]

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DLOG.  Note B18

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Given the foregoing explanation of the k-fold boundary operator,
along with its use to express such forms of logical constraints
as "just 1 of k is false" and "just 1 of k is true", there will
be no trouble interpreting an expression of the following shape
from the Jets and Sharks example:

   (( 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 ))

This expression says that everything in the universe of discourse
is either Art, or Al, or ..., or Neal, or Dave, but never any two
of them at once.  In effect, I've exploited the circumstance that
the universe contains but finitely many ostensible individuals to
to dedicate its own predicate to each one of them, demanding only
that these predicates be disjoint and exhaustive across the space.

Likewise, each of the following clauses has the effect of
partitioning the universe of discourse among the features
that are listed in the expression.

   ( jets , sharks )

   (( 20's ),( 30's ),( 40's ))

   (( junior_high ),( high_school ),( college ))

   (( single ),( married ),( divorced ))

   (( bookie ),( burglar ),( pusher ))

We may note in passing that ( x , y ) = ((x),(y)),
but this only holds for the 2-fold boundary operator.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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