I think this should work:
vocab = {'A','B','C','D'} % 1-by-M cell array of strings
P = {{'A'} ; {'C','A'} ; {'B','A'}} % N-by-1 cell array of cell array of strings
X = arrayfun(@(k) ismember(vocab, P{k,1}), 1:size(P,1), 'un', 0) ;
X = cat(1,X{:}) % a N-by-M logical array