Hello,
In the slide 22 of the Probabilistic Parsing lecture, it is mentioned that v_i = max(v_i, v_j*v_k*rho_i). Here, by v_i, we are referring to each non terminal present in cell i, right?
Thank You
Yes almost but not exactly: more precisely in the formula you mention 
refers to the maximum probability of "element i" (as mentioned above), which indeed is a non-terminal in a cell. This max-proba is the proba of the most probable parse that has root "element i" (a non-terminal, thus) in that cell (= covering the corresponding word subsequence).
The reason why we are here refering to "element i" rather than "non-terminal i" is simply because of a generalization of CYK (known as "bottom-up chart parsing") which was not covered in class this year (see https://moodlearchive.epfl.ch/2019-2020/mod/forum/discuss.php?d=22624#p44581).
Does it make more sense?
Yes, it is clearer to me now. Thank you for your answer!
