From 7a900fd39ba52da165cad37863e138bcfa04331f Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Mon, 5 May 2025 08:52:04 +0200 Subject: [PATCH] vault backup: 2025-05-05 08:52:04 --- .obsidian/workspace.json | 5 ++--- .../notes/15 - A formal language for LTSs.md | 5 ++++- Pasted image 20250505084741.png | Bin 0 -> 41278 bytes 3 files changed, 6 insertions(+), 4 deletions(-) create mode 100644 Pasted image 20250505084741.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index c8ca628..a9bcaab 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,9 +213,10 @@ }, "active": "cdcc59f1bf6d4ae1", "lastOpenFiles": [ - "Pasted image 20250505084556.png", "Concurrent Systems/slides/class 15.pdf", "Concurrent Systems/notes/15 - A formal language for LTSs.md", + "Pasted image 20250505084741.png", + "Pasted image 20250505084556.png", "Pasted image 20250505083948.png", "Pasted image 20250505083500.png", "Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md", @@ -235,8 +236,6 @@ "Concurrent Systems/notes/images/Pasted image 20250415082906.png", "Concurrent Systems/slides/class 14.pdf", "Concurrent Systems/notes/images/Pasted image 20250429092543.png", - "Concurrent Systems/notes/images/Pasted image 20250429092305.png", - "Concurrent Systems/notes/images/Pasted image 20250429092055.png", "Concurrent Systems/slides/class 12.pdf", "HCIW/slides/HCI in the car.pdf", "Concurrent Systems/slides/class 11.pdf", diff --git a/Concurrent Systems/notes/15 - A formal language for LTSs.md b/Concurrent Systems/notes/15 - A formal language for LTSs.md index d712010..be6cb9e 100644 --- a/Concurrent Systems/notes/15 - A formal language for LTSs.md +++ b/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 $\lnot \lozenge a p$ \ No newline at end of file +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 $$\forall P': P \xrightarrow{a} P' \implies P' \models \phi$$ diff --git a/Pasted image 20250505084741.png b/Pasted image 20250505084741.png new file mode 100644 index 0000000000000000000000000000000000000000..39df031ba128baee14110a13d87f527bc258da55 GIT binary patch literal 41278 zcmb@t^Lr*f&^LP5?$)+#+qP}n#@06Pa%`@aItMMl>h06-r8p9Gdc zkBkohkN{*QL^XW!u6n(F2-ke~1OrcIuY324y?;W&rkdR3qfzQ+GIWko1|HtXH{~8} 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