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Applied to a given proposition ''f'', the qualifiers &alpha;<sub>''i''</sub> and &beta;<sub>''i''</sub> tell whether ''f'' rests "above ''f''<sub>''i''</sub>" or "below ''f''<sub>''i''</sub>", respectively, in the implication ordering.  By way of example, let us trace the effects of several such measures, namely, those that occupy the limiting positions of the Tables.
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Applied to a given proposition <math>f,\!</math> the qualifiers <math>\alpha_i\!</math> and <math>\beta_i\!</math> tell whether <math>f\!</math> rests <math>\operatorname{above}\ f_i</math> or <math>\operatorname{below}\ f_i,</math> respectively, in the implication ordering.  By way of example, let us trace the effects of several such measures, namely, those that occupy the limiting positions of the Tables.
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{| cellpadding=2
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{| cellpadding="2"
 
| width="36" | &nbsp;
 
| width="36" | &nbsp;
| &alpha;<sub>00</sub>&nbsp;''f'' = 1
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| <math>\alpha_{00} f = 1\!</math>
| iff || ''f''<sub>00</sub> &rArr; ''f'',
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| iff   || <math>f_{00} \Rightarrow f,</math>
| iff || 0 &rArr; ''f'',
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| iff   || <math>0 \Rightarrow f,</math>
| hence || &alpha;<sub>00</sub>&nbsp;''f'' = 1 for all ''f''.
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| hence || <math>\alpha_{00} f = 1\ \operatorname{for~all}\ f.</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
| &alpha;<sub>15</sub>&nbsp;''f'' = 1
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| <math>\alpha_{15} f = 1\!</math>
| iff || ''f''<sub>15</sub> &rArr; f,
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| iff   || <math>f_{15} \Rightarrow f,</math>
| iff || 1 &rArr; ''f'',
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| iff   || <math>1 \Rightarrow f,</math>
| hence || &alpha;<sub>15</sub>&nbsp;''f'' = 1 &rArr; ''f'' = 1.
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| hence || <math>\alpha_{15} f = 1 \Rightarrow f = 1.</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
| &beta;<sub>00</sub>&nbsp;''f'' = 1
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| <math>\beta_{00} f = 1\!</math>
| iff || ''f'' &rArr; f<sub>00</sub>,
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| iff   || <math>f \Rightarrow f_{00},</math>
| iff || ''f'' &rArr; 0,
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| iff   || <math>f \Rightarrow 0,</math>
| hence || &beta;<sub>00</sub>&nbsp;''f'' = 1 &rArr; f = 0.
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| hence || <math>\beta_{00} f = 1 \Rightarrow f = 0.</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
| &beta;<sub>15</sub>&nbsp;''f'' = 1
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| <math>\beta_{15} f = 1\!</math>
| iff || ''f'' &rArr; f<sub>15</sub>,
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| iff   || <math>f \Rightarrow f_{15},</math>
| iff || ''f'' &rArr; 1,
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| iff   || <math>f \Rightarrow 1,</math>
| hence || &beta;<sub>15</sub>&nbsp;''f'' = 1 for all ''f''.
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| hence || <math>\beta_{15} f = 1\ \operatorname{for~all}\ f.</math>
 
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|}<br>
  
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