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95 lines
1.9 KiB
95 lines
1.9 KiB
\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\forall x$
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[.$\exists y$
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[.$\land$
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[.$P$ $x$ $y$ ]
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[.$Q$ $x$ ]
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]
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]
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]
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\end{tikzpicture}
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\begin{multicols}{2}
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\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\exists y$
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[.$\land$
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[.$P$ $a$ $y$ ]
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[.$Q$ $a$ ]
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]
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]
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\end{tikzpicture}
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\newline
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Subtree: $x=a$ \\
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\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\land$
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[.$P$ $a$ $a$ ]
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[.$Q$ $a$ ]
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]
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\end{tikzpicture}
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\newline
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Subtree: $x=a \land y=a$ \\
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Evaluates $\mathcal{M}_1$ to true. \\
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Evaluates $\mathcal{M}_2$ to false.
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\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\land$
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[.$P$ $a$ $b$ ]
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[.$Q$ $a$ ]
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]
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\end{tikzpicture}
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\newline
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Subtree: $x=a \land y=b$ \\
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Evaluates $\mathcal{M}_1$ to true. \\
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Evaluates $\mathcal{M}_2$ to false.
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\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\exists y$
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[.$\land$
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[.$P$ $b$ $y$ ]
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[.$Q$ $b$ ]
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]
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]
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\end{tikzpicture}
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\newline
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Subtree: $x=b$ \\
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\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\land$
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[.$P$ $b$ $a$ ]
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[.$Q$ $b$ ]
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]
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\end{tikzpicture}
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\newline
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Subtree: $x=b \land y=a$ \\
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Evaluates $\mathcal{M}_1$ to true. \\
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Evaluates $\mathcal{M}_2$ to false.
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\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\land$
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[.$P$ $b$ $b$ ]
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[.$Q$ $b$ ]
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]
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\end{tikzpicture}
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\newline
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Subtree: $x=b \land y=b$ \\
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Evaluates $\mathcal{M}_1$ to true. \\
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Evaluates $\mathcal{M}_2$ to false.
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\end{multicols}
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$\mathcal{M}_1: \mathcal{A} = \{a, b\}$ \\
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$P$ = true \\
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$Q$ = true \\
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$\mathcal{M}_1 \models \phi$ \\
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$\mathcal{M}_2: \mathcal{A} = \{a, b\}$ \\
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$P$ = true \\
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$Q$ = false \\
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$\mathcal{M}_2 \not\models \phi$
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