Changes

The next transformation of the source proposition <math>q,\!</math> that we are typically aiming to contemplate in the process of carrying out a ''differential analysis'' of its ''dynamic'' effects or implications, is the yield of the so-called ''difference'' or ''delta'' operator <math>\operatorname{D}.</math>  The resultant ''difference proposition'' <math>\operatorname{D}q</math> is defined in terms of the source proposition <math>q\!</math> and the ''shifted proposition'' <math>\operatorname{E}q</math> thusly:

The next transformation of the source proposition <math>q,\!</math> that we are typically aiming to contemplate in the process of carrying out a ''differential analysis'' of its ''dynamic'' effects or implications, is the yield of the so-called ''difference'' or ''delta'' operator <math>\operatorname{D}.</math>  The resultant ''difference proposition'' <math>\operatorname{D}q</math> is defined in terms of the source proposition <math>q\!</math> and the ''shifted proposition'' <math>\operatorname{E}q</math> thusly:

<pre>

<pre>

            Eq  q        Eq  eq

              o---o          o---o

              \ /            \ /

    Dq  =      @      =      @

    Dq  =  ( Eq , q )  =  ( Eq , eq ).

  |          Eq  q        Eq  eq

  |          o---o          o---o

  |            \ /            \ /

  | Dq  =      @      =      @

  | Dq  =  ( Eq , q )  =  ( Eq , eq ).

The result of applying the difference operator D to the source

Recall that a <math>k</math>-place bracket "<math>(x_1, x_2, \ldots, x_k)\!</math>" is interpreted (in the ''existential interpretation'') to mean "Exactly one of the <math>x_j\!</math> is false", thus the two-place bracket is equivalent to the exclusive-or.

proposition q, conjoined with a query on the center cell c, is:

o-------------------------------------------------o

o-------------------------------------------------o

| Dq.uvw                                          |

| Dq.uvw                                          |