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Directory:Jon Awbrey/Papers/Functional Logic : Quantification Theory (view source)
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, 20:38, 20 November 2008no edit summary
Tables 8 and 9 develop these ideas in more detail.
Tables 8 and 9 develop these ideas in more detail.
{| align="center" border="1" cellpadding="6" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="font-weight:bold; text-align:center; width:90%"
|+ '''Table 8. Relation of Quantifiers to Higher Order Propositions'''
|+ '''Table 8. Relation of Quantifiers to Higher Order Propositions'''
|- style="background:ghostwhite"
|- style="background:ghostwhite"
|Mnemonic||Category||Classical Form||Alternate Form||Symmetric Form||Operator
| Mnemonic
| Category
| Classical Form
| Alternate Form
| Symmetric Form
| Operator
|-
|-
| <math>\mathrm{E}\!</math><br>Exclusive
| <math>\mathrm{E}\!</math><br>Exclusive
| Universal<br>Negative
| Universal<br>Negative
| align=left | All x is (y)
| <math>\mbox{All } x \mbox{ is } (y)</math>
|
| align=left | No x is y
| <math>\mbox{No } x \mbox{ is } y</math>
| <math>(\!| \ell_{11} |\!)</math>
| <math>(\!| \ell_{11} |\!)</math>
|-
|-
| <math>\mathrm{A}\!</math><br>Absolute
| <math>\mathrm{A}\!</math><br>Absolute
| Universal<br>Affirmative
| Universal<br>Affirmative
| align=left | All x is y
| <math>\mbox{All } x \mbox{ is } y</math>
|
| align=left | No x is (y)
| <math>\mbox{No } x \mbox{ is } (y)</math>
| <math>(\!| \ell_{10} |\!)</math>
| <math>(\!| \ell_{10} |\!)</math>
|-
|-
|
|
|
|
| align=left | All y is x
| <math>\mbox{All } y \mbox{ is } x</math>
| align=left | No y is (x)
| <math>\mbox{No } y \mbox{ is } (x)</math>
| align=left | No (x) is y
| <math>\mbox{No } (x) \mbox{ is } y</math>
| <math>(\!| \ell_{01} |\!)</math>
| <math>(\!| \ell_{01} |\!)</math>
|-
|-
|
|
|
|
| align=left | All (y) is x
| <math>\mbox{All } (y) \mbox{ is } x</math>
| align=left | No (y) is (x)
| <math>\mbox{No } (y) \mbox{ is } (x)</math>
| align=left | No (x) is (y)
| <math>\mbox{No } (x) \mbox{ is } (y)</math>
| <math>(\!| \ell_{00} |\!)</math>
| <math>(\!| \ell_{00} |\!)</math>
|-
|-
|
|
|
|
| align=left | Some (x) is (y)
| <math>\mbox{Some } (x) \mbox{ is } (y)</math>
|
| align=left | Some (x) is (y)
| <math>\mbox{Some } (x) \mbox{ is } (y)</math>
| <math>\ell_{00}\!</math>
| <math>\ell_{00}\!</math>
|-
|-
|
|
|
|
| align=left | Some (x) is y
| <math>\mbox{Some } (x) \mbox{ is } y</math>
|
| align=left | Some (x) is y
| <math>\mbox{Some } (x) \mbox{ is } y</math>
| <math>\ell_{01}\!</math>
| <math>\ell_{01}\!</math>
|-
|-
| <math>\mathrm{O}\!</math><br>Obtrusive
| <math>\mathrm{O}\!</math><br>Obtrusive
| Particular<br>Negative
| Particular<br>Negative
| align=left | Some x is (y)
| <math>\mbox{Some } x \mbox{ is } (y)</math>
|
| align=left | Some x is (y)
| <math>\mbox{Some } x \mbox{ is } (y)</math>
| <math>\ell_{10}\!</math>
| <math>\ell_{10}\!</math>
|-
|-
| <math>\mathrm{I}\!</math><br>Indefinite
| <math>\mathrm{I}\!</math><br>Indefinite
| Particular<br>Affirmative
| Particular<br>Affirmative
| align=left | Some x is y
| <math>\mbox{Some } x \mbox{ is } y</math>
|
| align=left | Some x is y
| <math>\mbox{Some } x \mbox{ is } y</math>
| <math>\ell_{11}\!</math>
| <math>\ell_{11}\!</math>
|}<br>
|}<br>