Changes

The models of <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> can be comprehended as follows:

The models of <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> can be comprehended as follows:

*<p>Working in the ''summary coefficient'' form of representation, if the coordinate list <math>\mathbf{x}\!</math> is a model of <math>q\!</math> in <math>X,\!</math> then one can construct a coordinate list <math>\operatorname{e}\mathbf{x}\!</math> as a model for <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> just by appending any combination of values for the differential variables in <math>\operatorname{d}\mathcal{X}.</math></p><p>For example, to focus once again on the center cell <math>c,\!</math> which happens to be a model of the proposition <math>q\!</math> in <math>X,\!</math> one can extend <math>c\!</math> in eight different ways into <math>\operatorname{E}X,\!</math> and thus get eight models of the tacit extension <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X.\!</math></p>

*<p>Working in the ''summary coefficient'' form of representation, if the coordinate list <math>\mathbf{x}\!</math> is a model of <math>q\!</math> in <math>X,\!</math> then one can construct a coordinate list <math>\operatorname{e}\mathbf{x}\!</math> as a model for <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> just by appending any combination of values for the differential variables in <math>\operatorname{d}\mathcal{X}.</math></p><p>For example, to focus once again on the center cell <math>c,\!</math> which happens to be a model of the proposition <math>q\!</math> in <math>X,\!</math> one can extend <math>c\!</math> in eight different ways into <math>\operatorname{E}X,\!</math> and thus get eight models of the tacit extension <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X.\!</math></p><p>It is a trivial exercise to write these out, but it is useful to do so at least once in order to see the patterns of data involved.</p><p>The tacit extensions of <math>c\!</math> that are models of <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> are as follows:</p>

<pre>

<pre>

     <u, v, w, du, dv, dw> =

     <u, v, w, du, dv, dw> =

     <1, 1, 1,  1,  1,  0>,

     <1, 1, 1,  1,  1,  0>,

     <1, 1, 1,  1,  1,  1>.

     <1, 1, 1,  1,  1,  1>.

2.  Working in the "conjunctive product" form of representation,

2.  Working in the "conjunctive product" form of representation,

     if the conjunct symbol x is a model of q in X, then one can

     if the conjunct symbol x is a model of q in X, then one can