Commit 7b92a6d7 by Ralf Jung

docs: update semantic entailment

 ... ... @@ -98,20 +98,22 @@ We can now define \emph{semantic} logical entailment. \typedsection{Interpretation of entailment}{\Sem{\vctx \mid \pfctx \proves \prop} : \mProp} \Sem{\vctx \mid \pfctx \proves \prop} \eqdef \Sem{\vctx \mid \prop \proves \propB} \eqdef \begin{aligned}[t] \MoveEqLeft \forall n \in \mathbb{N}.\; \forall \rs \in \textdom{Res}.\; \forall \gamma \in \Sem{\vctx},\; \\& \bigl(\All \propB \in \pfctx. n \in \Sem{\vctx \proves \propB : \Prop}_\gamma(\rs)\bigr) \Ra n \in \Sem{\vctx \proves \prop : \Prop}_\gamma(\rs) n \in \Sem{\vctx \proves \prop : \Prop}_\gamma(\rs) \Ra n \in \Sem{\vctx \proves \propB : \Prop}_\gamma(\rs) \end{aligned} The soundness statement of the logic reads $\vctx \mid \pfctx \proves \prop \Ra \Sem{\vctx \mid \pfctx \proves \prop}$ The following theorem connects syntactic and semantic entailment: $\vctx \mid \prop \proves \propB \Ra \Sem{\vctx \mid \prop \proves \propB}$ It now becomes trivial to show soundness of the logic. %%% Local Variables: %%% mode: latex ... ...
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