On 5 March 2014 04:18, Bruno Marchal <[email protected]> wrote: > > Good. > > To prove that P -> Q, you can prove that P & ~Q leads to a contradiction, > or you can prove that ~Q leads to ~P. > > But it helps a lot if you start from what you want to prove, up to the > conclusion, so that not only you prove it, but you know exactly what you > discovered. In this case a necessary link, in Kripke semantics, between a > binary relation (reflexivity) and a modal formula []A->A. >
I had to get my head around ... well, everything ... again. So I may have sneaked up on the result. > > You learned that the fact that (W, R) respects []A -> A is equivalent with > the fact that R is reflexive. > > OK? > > OK. So, the next question was A Kripke multiverse (W, R) is said transitive if R is transitive. That is > > alpha R beta, and beta R gamma entails alpha R gamma, for all alpha beta > and gamma in W. > > Show that > > (W, R) respects []A -> [][]A if and only R is transitive, > Damn. This looks too complicated for me to fake it! -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
