Logichard
0:00.0

Let the set of worlds in a Kripke frame be W={w1,w2,w3}W = \{w_1, w_2, w_3\}, and let the accessibility relation be R={(w1,w2),(w2,w3),(w3,w1)}R = \{(w_1, w_2), (w_2, w_3), (w_3, w_1)\}. The valuation of a formula PP is V(P)={w1,w2}V(P) = \{w_1, w_2\}. Recall that wV(ϕ)w \in V(\Box \phi) if and only if for all uWu \in W such that (w,u)R(w, u) \in R, we have uV(ϕ)u \in V(\phi). What is the set of worlds where the modal formula (P    P)\Box(\Box P \implies P) is true?