u/ohmypix

I’m studying frames in model logic and the case where R is a euclidean relation means that:
possible p —> necessary( possible p)

however when i’m looking at the worlds, my understanding js the definition of Euclidean is
if Rwu and Rwv, then Ruv.

as a consequence, also Rvu

so if in w: possible p, p is then true in at least one world accessible form w. I’m gonna to say p true at u and p false at v as my example.

then, for possible p —> necessary (possible p) to hold, I can see at v, possible p is true, but at u it seems possible p does not hold since p is not true at v and u doesn’t have any other accessible worlds? Since it doesn’t hold for both u,v then not necessary (possible p))

i’d greatly appreciate any help