We encode the FOL rules using soft logic (Bach et al., 2015) for flexible encoding and stable optimization.
soft logic allows continuous truth values from the interval [0, 1] instead of {0, 1}, and the Boolean logic operators are reformulated as: Here & and ∧ are two different approximations to logical conjunction (Foulds et al., 2015): & is useful as a selection operator (e.g., A&B = B when A = 1, and A&B = 0 when A = 0), while ∧ is an averaging operator.