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Concurrent Systems/notes/15 - A formal language for LTSs.md

@@ -25,3 +25,10 @@ Another very useful logical operator is "box": let us define $\lnot \lozenge a p
 ![](../../Pasted%20image%2020250505084741.png)
 
 From the last condition, we have that $P $\models \square a \phi$ if and only if $$\forall P': P \xrightarrow{a} P' \implies P' \models \phi$$
+EXAMPLE: Let us now consider formula ☐aFF
+By definition, this happens only if, for every P’ resulting from P after action a, it holds P’ |= FF
+
+However, this can never happen, whatever P’ be;
+hence, P |= ☐aFF holds true only if P cannot perform any action a
+
+![](../../Pasted%20image%2020250505085454.png)