MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
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, 16:10, 4 February 2009
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− | The dyadic relation <math>L_{IS}\!</math> that makes up the converse of the connotative relation <math>L_{SI}\!</math> can be defined directly in the following fashion: | + | '''Editing Note.''' Need a discussion of converse relations here. Perhaps it would work to introduce the operators that Peirce used for the converse of a dyadic relative <math>\ell,</math> namely, <math>K\ell ~=~ k\!\cdot\!\ell ~=~ \breve\ell.</math> |
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| + | The dyadic relation <math>L_{IS}\!</math> that is the converse of the connotative relation <math>L_{SI}\!</math> can be defined directly in the following fashion: |
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| {| align="center" cellpadding="8" width="90%" | | {| align="center" cellpadding="8" width="90%" |
− | | <math>\widehat{\operatorname{Con} (L)} ~=~ L_{IS} ~=~ \{ (i, s) \in I \times S ~:~ (o, s, i) \in L ~\text{for some}~ o \in O \}.</math> | + | | <math>\overset{\smile}{\operatorname{Con}(L)} ~=~ L_{IS} ~=~ \{ (i, s) \in I \times S ~:~ (o, s, i) \in L ~\text{for some}~ o \in O \}.</math> |
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| A few of the many different expressions for this concept are recorded in Definition 9. | | A few of the many different expressions for this concept are recorded in Definition 9. |
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| <pre> | | <pre> |
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− | Recall the definition of Den(R), the denotative component of R, in the following form: | + | |
− | Den(R) = ROS = {<o, s> C OxS : <o, s, i> C R for some i C I}. | + | Recall the definition of <math>\operatorname{Den} (L),</math> the denotative component of <math>L,\!</math> in the following form: |
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| + | {| align="center" cellpadding="8" width="90%" |
| + | | <math>\operatorname{Den} (L) ~=~ L_{OS} ~=~ \{ (o, s) \in O \times S ~:~ (o, s, i) \in L ~\text{for some}~ i \in I \}.</math> |
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| Equivalent expressions for this concept are recorded in Definition 10. | | Equivalent expressions for this concept are recorded in Definition 10. |
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| + | <pre> |
| Definition 10 | | Definition 10 |
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