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\subsubsection{Requirements for a deductive system}
The derivation rules (syntactic entailment) and truth tables (semantic entailment) should agree.
For that we have two requirements, for $\Gamma = A_1, \ldots, A_n$ a collection of formulas:
\begin{itemize}
    \item \bi{Soundness:} If $\Gamma \vdash A$ can be derived, then $\Gamma \models A$
    \item \bi{Completeness:} If $\Gamma \models A$, then $\Gamma \vdash A$ can be derived
\end{itemize}

\bi{Decidability} is also desirable, i.e. having checks of the attributes be of low complexity.
