From 13fbfd08eccb35e42d2a8e5dbaca9701df17bc5f Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Mon, 5 May 2025 08:47:04 +0200 Subject: [PATCH] vault backup: 2025-05-05 08:47:04 --- .obsidian/workspace.json | 4 ++-- .../notes/15 - A formal language for LTSs.md | 7 ++++++- Pasted image 20250505084556.png | Bin 0 -> 129431 bytes 3 files changed, 8 insertions(+), 3 deletions(-) create mode 100644 Pasted image 20250505084556.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index aa2c3f5..c8ca628 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,9 +213,10 @@ }, "active": "cdcc59f1bf6d4ae1", "lastOpenFiles": [ - "Pasted image 20250505083948.png", + "Pasted image 20250505084556.png", "Concurrent Systems/slides/class 15.pdf", "Concurrent Systems/notes/15 - A formal language for LTSs.md", + "Pasted image 20250505083948.png", "Pasted image 20250505083500.png", "Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md", "Concurrent Systems/notes/12b - CCS cose varie.md", @@ -236,7 +237,6 @@ "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/notes/images/Pasted image 20250429091959.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 151e6d4..d712010 100644 --- a/Concurrent Systems/notes/15 - A formal language for LTSs.md +++ b/Concurrent Systems/notes/15 - A formal language for LTSs.md @@ -16,4 +16,9 @@ The language generated by this grammar will be denoted by Form; every element of ![](../../Pasted%20image%2020250505083948.png) -To simplify the proofs, we consider a more general form of conjunction: $\land_{i \in I, \phi i}$ \ No newline at end of file +To simplify the proofs, we consider a more general form of conjunction: $$\land_{i \in I, \phi_{i}}$$ +where I is any indexing set (possibility, also infinite). Satisfiability for this operator is similar to that for the binary operator. + +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 diff --git a/Pasted image 20250505084556.png b/Pasted image 20250505084556.png new file mode 100644 index 0000000000000000000000000000000000000000..8ab6e7cabcc80c13302025ffacd6f2da3997200e GIT binary patch literal 129431 zcma&NRZt~7&@H-wjmvD@VdL(DJA=EsyE_bnySux)ySohTHnoVtIVx^-Xf zLpn)Uo>J-b%IcK}MR^Hi1Uv))0DvqdDXI(r0O2Xf9n9N;G$>RRKOcbrt__XSo)beM#{L^8c8j zvdBzm<^MbXZ{+Ry|6LUJ|7Q{G-yx<13aP)p^bNUD0m5+FoZ6;B>R>6fz$CcH0%o{? zehbI|hA2KJQu5$@E~LObB{l)9u|{%d%v7_=UHVjLsZY!F<$q$WLZSgitTI)5!^65n1B!{iG4Vx}lDWl% zO>tx_gO<@9tx+)_*F;qpTz-t7X#ZX)VOhhU!h!jMVWLc^Dn7EGnwrtgm2N;%fCPL4 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