Dear Professor:
I am a university student in China and study on MLN recently;
I have a question as follow:
The joint distribution represented by a Markov network is given by $$P(X=x) = frac{1}{Z} prod_k phi_{k}(x_{{k}}) ag{2.1}$$ $$P(X=x) = frac{1}{Z} expleft(sum_j w_jf_j(x)
ight) ag{2.2}$$
The probability distribution over possible worlds x specified by the ground Markov network $M_{L, C}$ is given by $$P(X=x) = frac{1}{Z} expleft(sum_i w_in_i(x)
ight) = frac{1}{Z}prod_i phi_{i}(x_{{i}})^{n_i(x)} ag{2.3}$$
The probability of a ground predicate $X_l$ when its Markov blanket $B_l$ is in state $b_l$ is $$P(X_l=x_l|B_l=b_l) = frac{exp(sum_{f_i in F_l} w_if_i(X_l=x_l, B_l=b_l)))}{exp(sum_{f_i in F_l} w_if_i(X_l=0, B_l=b_l))+exp(sum_{f_i in F_l} w_if_i(X_l=1, B_l=b_l))} ag{3.3}$$
I can't figure out how to derive equation(3.3) from equation(2.1) or equation(2.3), maybe equation(3.3) is a definition, not a derivation ??