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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 17:44, 20 May 2013
, 17:44, 20 May 2013→6.43. Reflective Extensions: markup
Against this background, other varieties of reflective extension can be specified by means of semantic equations that are considered to be imposed on the elements of <math>F.\!</math> Taking the reflective extensions <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B})\!</math> as the first orders of a “free” project toward reflective closure, variant extensions can be described by relating their entries with those of comparable members in the standard sequences <math>\operatorname{Ref}^n (\text{A})\!</math> and <math>\operatorname{Ref}^n (\text{B}).\!</math>
Against this background, other varieties of reflective extension can be specified by means of semantic equations that are considered to be imposed on the elements of <math>F.\!</math> Taking the reflective extensions <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B})\!</math> as the first orders of a “free” project toward reflective closure, variant extensions can be described by relating their entries with those of comparable members in the standard sequences <math>\operatorname{Ref}^n (\text{A})\!</math> and <math>\operatorname{Ref}^n (\text{B}).\!</math>
A variant pair of reflective extensions, <math>\operatorname{Ref}^1 (\text{A} | E_1)\!</math> and <math>\operatorname{Ref}^1 (\text{B} | E_1),\!</math> are presented in Tables 82 and 83, respectively. These are identical to the corresponding free variants, <math>\operatorname{Ref}^1 (\text{A})\!</math> and <math>\operatorname{Ref}^1 (\text{B}),\!</math> with the exception of those entries that are constrained by the following system of semantic equations.
<pre>
<pre>
E1: <<A>> = <A>, <<B>> = <B>, <<i>> = <i>, <<u>> = <u>.
E1: <<A>> = <A>, <<B>> = <B>, <<i>> = <i>, <<u>> = <u>.