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Revision as of 01:14, 7 May 2008
, 01:14, 7 May 2008→Note 18: markup
===Note 18===
===Note 18===
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:
<pre>
<pre>
(( art ),( al ),( sam ),( clyde ),( mike ),
(( art ),( al ),( sam ),( clyde ),( mike ),
( jim ),( greg ),( john ),( doug ),( lance ),
( jim ),( greg ),( john ),( doug ),( lance ),
( karl ),( ken ),( earl ),( rick ),( ol ),
( karl ),( ken ),( earl ),( rick ),( ol ),
( neal ),( dave ))
( neal ),( dave ))
</pre>
This expression says that everything in the universe of discourse
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 dedicate its own predicate to each one of them, imposing only the requirement that these predicates must be disjoint and exhaustive.
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
dedicate its own predicate to each one of them, imposing only the
requirement that these predicates must be disjoint and exhaustive.
Likewise, each of the following clauses has the effect of
Likewise, each of the following clauses has the effect of partitioning the universe of discourse among the factions or features that are enumerated in the clause in question.
partitioning the universe of discourse among the factions
or features that are enumerated in the clause in question.
<pre>
( jets , sharks )
( jets , sharks )
(( 20's ),( 30's ),( 40's ))
(( 20's ),( 30's ),( 40's ))
(( junior_high ),( high_school ),( college ))
(( junior_high ),( high_school ),( college ))
(( single ),( married ),( divorced ))
(( single ),( married ),( divorced ))
(( bookie ),( burglar ),( pusher ))
(( bookie ),( burglar ),( pusher ))
</pre>
We may note in passing that ( x , y ) = ((x),(y)),
We may note in passing that <math>(x, y) = ((x),(y)),\!</math> but a rule of this form holds only in the case of the 2-fold boundary operator.
but a rule of this form holds only in the case of
the 2-fold boundary operator.
===Note 19===
===Note 19===
