SUO: Re: Examples! Examples! Examples!
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EEE. Note 20
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In referring to an element x of the 25-dimensional B-valued model space,
or more preciously the space of interpretations TLC = <|a_1, ..., a_25|>,
we have the following two options:
1. Denote x by means of a coordinate sequence:
x = <x_1, ..., x_25> in B^25.
2. Denote x by means of a conjunctive expression:
x = Prod_j (j = 1 to 25) e_j
where e_j = (a_j) if x_j = 0,
and e_j = a_j if x_j = 1.
Option (1) is called the "coordinate representation" and
option (2) is called the "conjunctive representation" of
the elements in TLC. The type of proposition that gets
generated under the conjunctive representation is also
called a "singular proposition", since it picks out
a single point of the model space.
The coordinate option is more compact, but its use depends on
remembering the verbose lexical terms that are abbreviated in
the forms of a_1, ..., a_25, and thus on what is described as
an "ordered basis". Then again, a bunch of boolean codes, if
you lose the key to their meanings, is a mess of useless bits.
Jon Awbrey
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