# LTL-CTL clarification

For translation logic, i want to know if any one of the below formulae are incorrect:

1) Fa & Fb & Fc = F(a & b & c)

2) F(a & b & c) = Fa & Fb & Fc

3) AFb=Fb

4)Fb=AFb

I think #2 and 4 are wrong, #1 and# 3 are right but I am not sure. Could you please clarify?

edited

+1 vote

They are all wrong, also #1 and #2 are the same just written the other way around, and also #3 and #4 are the same. #3 and #4 compare state and path formulas, which can never be the same.
by (166k points)
selected by
If 3 & 4 are wrong, then why it is solved that way in 2021.08.27 paper?(First questions) AG((AFa) & (AFb) & (AFc)) =>AG((Fa) & (Fb) & (Fc))?
which problem is that in the 2021.08.27 paper?
do you mean the 2019.08.27 paper?
It seems the paper is of 2021.02, however the question paper is wrongly dated as 2021.08, I have attached the question screenshot in the edited question, plaese have a look.

Translation Logic - Question 8-a 2021.02
Okay, I found it now. The point is that we have AGphi = AGAphi, so that we can translate AG(Fa&Fb) to AGA(Fa&Fb) and then to AG((AFa)&(AFb)). Still that does not mean that Fa is equivalent to AFa. Both are just the same under the context of AG, but not in general.
This is what my second guess when arriving to this solution when you said AFa!=Fa as I was aware about AGphi=AGAphi. It is now clear to me how this is solved.
Thank you very much for clarifying.