Syntactically, an MLN consists of a set of firstorder logical formulas F and a real-valued weight w F for each F ∈ F. Semantically, an MLN defines a probability distribution over possible groundings of the logical formulas.
if U denotes the set of all objects in the universe, and G denotes the set of all possible ways to ground every F ∈ F (i.e., substitute an element from U for every variable in F ), then an MLN defines a distribution over truth assignments to the grounded formulas G ∈ G. Let I denote the set of all possible interpretations of G -that is, each I ∈ I assigns true or false to every G ∈ G. The probability of a particular interpretation I according to the MLN is given by : where n(F, I) gives the number of groundings of F that are true in interpretation I.