Changes

With this interpretation in mind we note the following correspondences between classical quantifications and higher order indicator functions:

With this interpretation in mind we note the following correspondences between classical quantifications and higher order indicator functions:

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|+ <math>\text{Table 7.} ~~ \text{Syllogistic Premisses as Higher Order Indicator Functions}</math>

|+ <math>\text{Table 7.} ~~ \text{Syllogistic Premisses as Higher Order Indicator Functions}</math>

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<math>\begin{array}{clcl}

<math>\begin{array}{clcl}

\mathrm{A}                           &

\mathrm{A}

\mathrm{Universal~Affirmative}       &

& \mathrm{Universal~Affirmative}

\mathrm{All}\ u\ \mathrm{is}\ v     &

& \mathrm{All} ~ u ~ \mathrm{is} ~ v

\mathrm{Indicator~of}\ u (v) = 0     \\

& \mathrm{Indicator~of} ~ u \texttt{(} v \texttt{)} = 0

\mathrm{E}                           &

\\

\mathrm{Universal~Negative}         &

\mathrm{E}

\mathrm{All}\ u\ \mathrm{is}\ (v)   &

& \mathrm{Universal~Negative}

\mathrm{Indicator~of}\ u \cdot v = 0 \\

& \mathrm{All} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}

\mathrm{I}                           &

& \mathrm{Indicator~of} ~ u \cdot v = 0

\mathrm{Particular~Affirmative}     &

\\

\mathrm{Some}\ u\ \mathrm{is}\ v     &

\mathrm{I}

\mathrm{Indicator~of}\ u \cdot v = 1 \\

& \mathrm{Particular~Affirmative}

\mathrm{O}                           &

& \mathrm{Some} ~ u ~ \mathrm{is} ~ v

\mathrm{Particular~Negative}         &

& \mathrm{Indicator~of} ~ u \cdot v = 1

\mathrm{Some}\ u\ \mathrm{is}\ (v)   &

\\

\mathrm{Indicator~of}\ u (v) = 1     \\

\mathrm{O}

& \mathrm{Particular~Negative}

& \mathrm{Some} ~ u ~ \mathrm{is} ~ \texttt{(} v \texttt{)}

& \mathrm{Indicator~of} ~ u \texttt{(} v \texttt{)} = 1

\end{array}</math>

\end{array}</math>

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