You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
73 lines
1.6 KiB
73 lines
1.6 KiB
\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.15cm]
|
|
\Tree
|
|
[.$\lor $
|
|
[.$\forall x$
|
|
[.$P$ $x$ $x$ ]
|
|
]
|
|
[.$\forall y$
|
|
[.$Q$ $x$ $y$ ]
|
|
]
|
|
]
|
|
\end{tikzpicture}
|
|
|
|
The $x$ in the right subformula is a free variable.
|
|
|
|
|
|
\begin{multicols}{2}
|
|
An example for a \emph{satisfying} model $\Model_{SAT}$:
|
|
\begin{itemize}
|
|
\item $\mathcal{A} = \{a, b\} $
|
|
\item $P^{\Model_{SAT}} = \{(a,a), (b,b)\}$
|
|
\item $Q^{\Model_{SAT}} = \{(a,a), (a,b)\}$
|
|
\end{itemize}
|
|
\columnbreak
|
|
An example for an \emph{unsatisfying} model $\Model_{UNSAT}$:
|
|
\begin{itemize}
|
|
\item $\mathcal{A} = \{a, b\} $
|
|
\item $P^{\Model_{UNSAT}} = \{(a,a)\}$
|
|
\item $Q^{\Model_{UNSAT}} = \{(a,a)\}$
|
|
\end{itemize}
|
|
\end{multicols}
|
|
|
|
|
|
\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
|
|
\Tree
|
|
[.$\lnot$
|
|
[.$\forall x$
|
|
[.$\land$
|
|
[.$\imp$
|
|
[.$Q$
|
|
[.$f$ $x$ ]
|
|
]
|
|
[.$P$
|
|
[.$f$
|
|
[.$f$ $x$ ]
|
|
]
|
|
]
|
|
]
|
|
[.$\lnot$
|
|
[.$Q$ $x$ ]
|
|
]
|
|
]
|
|
]
|
|
]
|
|
|
|
|
|
\end{tikzpicture}
|
|
\begin{multicols}{2}
|
|
An example for a \emph{satisfying} model $\Model_{SAT}$:
|
|
\begin{itemize}
|
|
\item $\mathcal{A} = \{a, b\} $
|
|
\item $f^{\Model_{SAT}} = \{ x \rightarrow x \}$
|
|
\item $P^{\Model_{SAT}} = \true$
|
|
\item $Q^{\Model_{SAT}} = \false$
|
|
\end{itemize}
|
|
\columnbreak
|
|
An example for an \emph{unsatisfying} model $\Model_{UNSAT}$:
|
|
\begin{itemize}
|
|
\item $\mathcal{A} = \{a, b\} $
|
|
\item $f^{\Model_{UNSAT}} = \{ x \rightarrow x \}$
|
|
\item $P^{\Model_{UNSAT}} = \true$
|
|
\item $Q^{\Model_{UNSAT}} = \false$
|
|
\end{itemize}
|
|
\end{multicols}
|