I have a question about the notion of possibility in modal logic. There are systems and worlds with this notion. They say that a world w1 is accessible to an other world w2 if and only if for any true proposition of w p be possible in w2. I also read about possible words of s5 system that have identical necessary an contingent propositions. Also these worlds are accessible worlds from each other. So i am confused. For example assume a world w3 that exist in it a 3-handed human being. A being that do not exist in the actual world w4. Assume q as a 3 handed human being exists. So we know by definition of contingency and possibility that q is contingent in both w3 and w4. And it seems that q is not possible in w4 actual world because q is false in it and possibility means to be consistent with the truths. It is not possible in w4 that q be true. We said q is contingent just because q is true in some equivalent accessible world w3. So knowing this come to return to the definition of accessibility or so-called relative possibility. We said a world is accessible to an other world if and only if any true p of the first is possible in latter. Who w3 and w4 will be accessible as they obviously claim in modal logic of s5 system and its possible worlds?
Does they mean contingency from possibility? If it is so does the quantifiers of the modal logic is necessity and contingency instead of the first and possibility??
https://en.wikipedia.org/wiki/Accessibility_relation to read about accessiblity realation