I am reading Brain Chellas' Modal Logic and have a question regarding point-wise and (simple) equivalence: what is a scenario in which two models are equivalent but not point-wise equivalent?
Say, for example, that we have two models such that:
M1 = <W: {1, 2, 3, 4, 5}, P: {{1}, {2, 3}, {5}}>
M2 = <W: {1, 2, 3, 4, 5}, P: {{2}, {3, 4}, {5}}>
M1
assigns p to {1}, q to {2, 3}, and r to {5} and M2
assigns p to {2}, q to {3, 4}, and r to {5}. Are the models point-wise equivalent? Are they (simply) equivalent? Why?
Any insight appreciated.