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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 20:40, 2 May 2008
, 20:40, 2 May 2008→Note 6: markup
The models of this last expression tell us which combinations of feature changes among the set <math>\{ \operatorname{d}u, \operatorname{d}v, \operatorname{d}w \}</math> will take us from our present interpretation, the center cell expressed by "<code>u v w</code>", to a true value under the given proposition <code>(( u v )( u w )( v w ))</code>.
The models of this last expression tell us which combinations of feature changes among the set <math>\{ \operatorname{d}u, \operatorname{d}v, \operatorname{d}w \}</math> will take us from our present interpretation, the center cell expressed by "<code>u v w</code>", to a true value under the given proposition <code>(( u v )( u w )( v w ))</code>.
The models of <math>\operatorname{E}q \cdot c</math> can be described in the usual ways as follows:
* The points of the space <math>\operatorname{E}X</math> that have the following coordinate descriptions:
<pre>
<pre>
<u, v, w, du, dv, dw> =
<u, v, w, du, dv, dw> =
<1, 1, 1, 0, 0, 0>,
<1, 1, 1, 0, 0, 0>,
<1, 1, 1, 0, 0, 1>,
<1, 1, 1, 0, 0, 1>,
<1, 1, 1, 0, 1, 0>,
<1, 1, 1, 0, 1, 0>,
<1, 1, 1, 1, 0, 0>.
<1, 1, 1, 1, 0, 0>.
</pre>
* The points of the space <math>\operatorname{E}X</math> that have the following conjunctive expressions:
<pre>
u v w (du)(dv)(dw),
u v w (du)(dv)(dw),
u v w (du)(dv) dw ,
u v w (du)(dv) dw ,
u v w (du) dv (dw),
u v w (du) dv (dw),
u v w du (dv)(dw).
u v w du (dv)(dw).
</pre>
<pre>
In summary, Eq.c informs us that we can get from c to a model of q by
In summary, Eq.c informs us that we can get from c to a model of q by
making the following changes in our position with respect to u, v, w,
making the following changes in our position with respect to u, v, w,