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in the given graph <>{s0,s4} = {s5} so simillarly what will be the <>{ } will it be { } or {s3,s2}

in * TF "Emb. Sys. and Rob." by (200 points)

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<> phi holds on the states that have a successor state which satisfies phi. With <>{}, I guess, you mean <>false which would hold on the states which would have a successor state where false holds. However, no state can satisfy false, and therefore <>false does not hold on any state, and therefore the states satisfying <>false are {}. This is independent of a Kripke structure.
by (170k points)
Thank You. And, what about universal predecessor for false?.
See slide 15 of the temporal logic chapter: []false holds on states with no successor states.
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