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Functional Logic • Inquiry and Analogy • 16

Higher Order Universe of Discourse

PNG

Higher Order Universe of Discourse
\text{Higher Order Universe of Discourse}~ [ \ell_{00}, \ell_{01}, \ell_{10}, \ell_{11} ] \subseteq [[ u, v ]]

JPG

Higher Order Universe of Discourse
\text{Higher Order Universe of Discourse}~ [ \ell_{00}, \ell_{01}, \ell_{10}, \ell_{11} ] \subseteq [[ u, v ]]

GIF

Higher Order Universe of Discourse
\text{Higher Order Universe of Discourse}~ [ \ell_{00}, \ell_{01}, \ell_{10}, \ell_{11} ] \subseteq [[ u, v ]]

\text{Qualifiers}~ \ell_{ij} : (\mathbb{B} \times \mathbb{B} \to \mathbb{B}) \to \mathbb{B}

PNG 2.0

Qualifiers ℓ_ij : (B × B → B) → B

PNG 1.0

Qualifiers ℓ_ij : (B × B → B) → B

LaTeX 2.0

\begin{array}{*{11}{l}} \ell_{00} f & = & \ell_{\texttt{(} u \texttt{)(} v \texttt{)}} f & = & \alpha_1 f & = & \Upsilon_{\texttt{(} u \texttt{)(} v \texttt{)}} f & = & \Upsilon_{\texttt{(} u \texttt{)(} v \texttt{)} \,\Rightarrow\, f} & = & f ~\text{likes}~ \texttt{(} u \texttt{)(} v \texttt{)} \\ \ell_{01} f & = & \ell_{\texttt{(} u \texttt{)} v} f & = & \alpha_2 f & = & \Upsilon_{\texttt{(} u \texttt{)} v} f & = & \Upsilon_{\texttt{(} u \texttt{)} v \,\Rightarrow\, f} & = & f ~\text{likes}~ \texttt{(} u \texttt{)} v \\ \ell_{10} f & = & \ell_{u \texttt{(} v \texttt{)}} f & = & \alpha_4 f & = & \Upsilon_{u \texttt{(} v \texttt{)}} f & = & \Upsilon_{u \texttt{(} v \texttt{)} \,\Rightarrow\, f} & = & f ~\text{likes}~ u \texttt{(} v \texttt{)} \\ \ell_{11} f & = & \ell_{u \, v} f & = & \alpha_8 f & = & \Upsilon_{u \, v} f & = & \Upsilon_{u \, v \,\Rightarrow\, f} & = & f ~\text{likes}~ u \, v \end{array}

LaTeX 1.0

\begin{array}{*{11}{l}} \ell_{00} f & = & \ell_{(u)(v)} f & = & \alpha_1 f & = & \Upsilon_{(u)(v)} f & = & \Upsilon_{(u)(v)\ \Rightarrow f} & = & f\ \mathrm{likes}\ (u)(v) \\ \ell_{01} f & = & \ell_{(u) v} f & = & \alpha_2 f & = & \Upsilon_{(u) v} f & = & \Upsilon_{(u) v\ \Rightarrow f} & = & f\ \mathrm{likes}\ (u) v \\ \ell_{10} f & = & \ell_{u (v)} f & = & \alpha_4 f & = & \Upsilon_{u (v)} f & = & \Upsilon_{u (v)\ \Rightarrow f} & = & f\ \mathrm{likes}\ u (v) \\ \ell_{11} f & = & \ell_{u v} f & = & \alpha_8 f & = & \Upsilon_{u v} f & = & \Upsilon_{u v\ \Rightarrow f} & = & f\ \mathrm{likes}\ u v \end{array}