I didn't understand what is mean Box T, diamond T in this example:
what is mean box True exist in world v?
2026-03-25 05:46:59.1774417619
Modal logic Box and diamond T
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According to the semantics, $$(M,w) \models \square \top \quad \mathrm{iff} \quad \forall v \in W: R(w, v) \ \mathrm{implies} \ (M,w) \models \top.$$ Since $\top$ is true everywhere, proposition $\square \top$ state a rather trivial validity: for all accessible states $\top$ holds there.
Diamond, however, is more informative. According to the semantics, $$(M,w) \models \Diamond \top \quad \mathrm{iff} \quad \exists v \in W: R(w, v) \ \mathrm{and} \ (M,w) \models \top.$$ Since $\top$ is true everywhere, proposition $\Diamond \top$ says that there is a transition from the given state.
Hope, that helps.