vault backup: 2025-05-05 08:52:04

.obsidian/workspace.json

@@ -213,9 +213,10 @@
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+    "Pasted image 20250505084556.png",
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@@ -235,8 +236,6 @@
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Concurrent Systems/notes/15 - A formal language for LTSs.md

@@ -21,4 +21,7 @@ where I is any indexing set (possibility, also infinite). Satisfiability for thi
 
 Of course, we can use the boolean constant FALSE (FF) and classical logical operators like disjunction $\lor$ and implication $=>$ (they can all be derived in the usual way from $TT, \lnot, \land$).
 
-Another very useful logical operator is "box": let us define $\lnot \lozenge a p$ 
+Another very useful logical operator is "box": let us define $\lnot \lozenge a p$ as $\square a \lnot \phi$
+![](../../Pasted%20image%2020250505084741.png)
+
+From the last condition, we have that $P $\models \square a \phi$ if and only if $$\forall P': P \xrightarrow{a} P' \implies P' \models \phi$$