Please identify the theorem and then prove it. Show that the modal system S4 is not identical to the modal system S5 by
Posted: Thu May 12, 2022 12:03 pm
Please identify the theorem and then prove it.
Show that the modal system S4 is not identical to the modal
system S5 by finding a theorem of S5 that is not a theorem S4.
Now show that the theorem of S5 you provided is not
valid in the class of S4 models. That is: produce a model
that contains a world such that: (i) the model has an accessibility
relation that is reflexive and transitive; and (ii) (an instance
of) your S5 theorem is false at that world.
Show that the modal system S4 is not identical to the modal
system S5 by finding a theorem of S5 that is not a theorem S4.
Now show that the theorem of S5 you provided is not
valid in the class of S4 models. That is: produce a model
that contains a world such that: (i) the model has an accessibility
relation that is reflexive and transitive; and (ii) (an instance
of) your S5 theorem is false at that world.