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Applied to a given proposition ''f'', the qualifiers &alpha;_''i'' and &beta;_''i'' tell whether ''f'' rests "above ''f''_''i''" or "below ''f''_''i''", 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.

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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| &alpha;₀₀&nbsp;''f'' = 1

| <math>\alpha_{00} f = 1\!</math>

| iff || ''f''₀₀ &rArr; ''f'',

| iff   || <math>f_{00} \Rightarrow f,</math>

| iff || 0 &rArr; ''f'',

| iff   || <math>0 \Rightarrow f,</math>

| hence || &alpha;₀₀&nbsp;''f'' = 1 for all ''f''.

| hence || <math>\alpha_{00} f = 1\ \operatorname{for~all}\ f.</math>

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| &nbsp;

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| &alpha;₁₅&nbsp;''f'' = 1

| <math>\alpha_{15} f = 1\!</math>

| iff || ''f''₁₅ &rArr; f,

| iff   || <math>f_{15} \Rightarrow f,</math>

| iff || 1 &rArr; ''f'',

| iff   || <math>1 \Rightarrow f,</math>

| hence || &alpha;₁₅&nbsp;''f'' = 1 &rArr; ''f'' = 1.

| hence || <math>\alpha_{15} f = 1 \Rightarrow f = 1.</math>

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| &beta;₀₀&nbsp;''f'' = 1

| <math>\beta_{00} f = 1\!</math>

| iff || ''f'' &rArr; f₀₀,

| iff   || <math>f \Rightarrow f_{00},</math>

| iff || ''f'' &rArr; 0,

| iff   || <math>f \Rightarrow 0,</math>

| hence || &beta;₀₀&nbsp;''f'' = 1 &rArr; f = 0.

| hence || <math>\beta_{00} f = 1 \Rightarrow f = 0.</math>

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| &beta;₁₅&nbsp;''f'' = 1

| <math>\beta_{15} f = 1\!</math>

| iff || ''f'' &rArr; f₁₅,

| iff   || <math>f \Rightarrow f_{15},</math>

| iff || ''f'' &rArr; 1,

| iff   || <math>f \Rightarrow 1,</math>

| hence || &beta;₁₅&nbsp;''f'' = 1 for all ''f''.

| hence || <math>\beta_{15} f = 1\ \operatorname{for~all}\ f.</math>

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