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Marco Realacci 2025-05-05 08:57:04 +02:00
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.obsidian/workspace.json vendored
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@ -213,6 +213,7 @@
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"Pasted image 20250505085454.png",
"Concurrent Systems/slides/class 15.pdf", "Concurrent Systems/slides/class 15.pdf",
"Concurrent Systems/notes/15 - A formal language for LTSs.md", "Concurrent Systems/notes/15 - A formal language for LTSs.md",
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Concurrent Systems/notes/15 - A formal language for LTSs.md
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@ -25,3 +25,10 @@ Another very useful logical operator is "box": let us define $\lnot \lozenge a p
![](../../Pasted%20image%2020250505084741.png) ![](../../Pasted%20image%2020250505084741.png)
From the last condition, we have that $P $\models \square a \phi$ if and only if $$\forall P': P \xrightarrow{a} P' \implies P' \models \phi$$ 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)

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