Where p designates some proposition, M designates a model and w designates a world. Sorry if this question is too basic, but I think it is so basic that none of the basic textbooks and articles which I have consulted give a clear explanation. I understand that the first formula expresses that p is true under model M, in world p. But what does the second formula express?
A different example is from epistemic logic. What is the difference between: M, w |= ￢Kap and M|￢Kap, w |= ￢Kap