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Revision as of 04:12, 4 February 2009
, 04:12, 4 February 2009→Derived Equivalence Relations: mathematical markup
In the following definitions, let <math>L \subseteq O \times S \times I,</math> let <math>S = I,\!</math> and let <math>x, y \in S.\!</math>
In the following definitions, let <math>L \subseteq O \times S \times I,</math> let <math>S = I,\!</math> and let <math>x, y \in S.\!</math>
Recall the definition of <math>\operatorname{Con} (L),</math> the connotative component of a sign relation <math>L,\!</math> in the following form:
Recall the definition of Con(R), the connotative component of R, in the following form:
{| align="center" cellpadding="8" width="90%"
| <math>\operatorname{Con} (L) ~=~ L_{SI} ~=~ \{ (s, i) \in S \times I ~:~ (o, s, i) \in L ~\text{for some}~ o \in O \}.</math>
|}
Equivalent expressions for this concept are recorded in Definition 8.
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<pre>
Definition 8
Definition 8
D8e. {<s, i> C SxI : <o, s, i> C R for some o C O}
D8e. {<s, i> C SxI : <o, s, i> C R for some o C O}
</pre>
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<pre>
The dyadic relation RIS that constitutes the converse of the connotative relation RSI can be defined directly in the following fashion:
The dyadic relation RIS that constitutes the converse of the connotative relation RSI can be defined directly in the following fashion: