Lets say we have model like the one above or a similar one where a node refers back to itself.
Now let's say if I want to know the validity of the formula:
$M, s_2 \models Xr$
Will this be valid or not. In my textbook it says :
$\pi \models X\phi$ iff $\pi^2 \models \phi$
If we are starting at state 2 then our path would be $S_2 -> S_2 -> ...$
So, I'm not sure since state 2 is not actually transitioning to another states like State 0 or 1. Otherwise would transitioning to the same state in a path $\pi$ be enough to satisfy the "X" connective.