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MyWikiBiz, Author Your Legacy — Thursday November 14, 2024
Jump to navigationJump to search→Functional Quantifiers: + table of simple qualifiers with props arranged by group orbits
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
|+ '''Table 4. Relation of Quantifiers to Higher Order Propositions'''
|+ '''Table 4. Simple Qualifiers of Propositions (''n'' = 2)'''
|- style="background:ghostwhite"
| align="right" | <math>u:</math><br><math>v:</math>
| 1100<br>1010
| <math>f\!</math>
| <math>(\ell_{11})</math><br><math>\text{No } u </math><br><math>\text{is } v </math>
| <math>(\ell_{10})</math><br><math>\text{No } u </math><br><math>\text{is }(v)</math>
| <math>(\ell_{01})</math><br><math>\text{No }(u)</math><br><math>\text{is } v </math>
| <math>(\ell_{00})</math><br><math>\text{No }(u)</math><br><math>\text{is }(v)</math>
| <math> \ell_{00} </math><br><math>\text{Some }(u)</math><br><math>\text{is }(v)</math>
| <math> \ell_{01} </math><br><math>\text{Some }(u)</math><br><math>\text{is } v </math>
| <math> \ell_{10} </math><br><math>\text{Some } u </math><br><math>\text{is }(v)</math>
| <math> \ell_{11} </math><br><math>\text{Some } u </math><br><math>\text{is } v </math>
|-
| <math>f_0</math>
| 0000
| <math>(~)</math>
| 1
| 1
| 1
| 1
|
|
|
|
|-
| <math>f_1</math>
| 0001
| <math>(u)(v)\!</math>
| 1
| 1
| 1
|
| 1
|
|
|
|-
| <math>f_2</math>
| 0010
| <math>(u) v\!</math>
| 1
| 1
|
| 1
|
| 1
|
|
|-
| <math>f_4</math>
| 0100
| <math>u (v)\!</math>
| 1
|
| 1
| 1
|
|
| 1
|
|-
| <math>f_8</math>
| 1000
| <math>u v\!</math>
|
| 1
| 1
| 1
|
|
|
| 1
|-
| <math>f_3</math>
| 0011
| <math>(u)\!</math>
| 1
| 1
|
|
| 1
| 1
|
|
|-
| <math>f_{12}</math>
| 1100
| <math>u\!</math>
|
|
| 1
| 1
|
|
| 1
| 1
|-
| <math>f_6</math>
| 0110
| <math>(u, v)\!</math>
| 1
|
|
| 1
|
| 1
| 1
|
|-
| <math>f_9</math>
| 1001
| <math>((u, v))\!</math>
|
| 1
| 1
|
| 1
|
|
| 1
|-
| <math>f_5</math>
| 0101
| <math>(v)\!</math>
| 1
|
| 1
|
| 1
|
| 1
|
|-
| <math>f_{10}</math>
| 1010
| <math>v\!</math>
|
| 1
|
| 1
|
| 1
|
| 1
|-
| <math>f_7</math>
| 0111
| <math>(u v)\!</math>
| 1
|
|
|
| 1
| 1
| 1
|
|-
| <math>f_{11}</math>
| 1011
| <math>(u (v))\!</math>
|
| 1
|
|
| 1
| 1
|
| 1
|-
| <math>f_{13}</math>
| 1101
| <math>((u) v)\!</math>
|
|
| 1
|
| 1
|
| 1
| 1
|-
| <math>f_{14}</math>
| 1110
| <math>((u)(v))\!</math>
|
|
|
| 1
|
| 1
| 1
| 1
|-
| <math>f_{15}</math>
| 1111
| <math>((~))</math>
|
|
|
|
| 1
| 1
| 1
| 1
|}<br>
{| align="center" border="1" cellpadding="2" cellspacing="0" style="font-weight:bold; text-align:center; width:96%"
|+ '''Table 5. Relation of Quantifiers to Higher Order Propositions'''
|- style="background:ghostwhite"
|- style="background:ghostwhite"
| <math>\text{Mnemonic}</math>
| <math>\text{Mnemonic}</math>
