The logarithmic additivity conjecture for algebraic fiber spaces

Let $f\colon X\to Y$ be an algebraic fiber space between smooth projective varieties. Let $E$ be a simple normal crossing divisor on $X$ and $D$ a simple normal crossing divisor on $Y$ such that

$$\operatorname{Supp}(f^*D)\subseteq E.$$

Assume that $f$ is log-smooth over $V=Y\smallsetminus D$, meaning that every stratum of $(X,E)$, including $X$, is smooth over $V$ via $f$. Let $F$ be a general fiber over a point of $V$, and write $E_F$ for the induced divisor on $F$. The logarithmic additivity conjecture. One should have

$$\kappa(X,K_X+E)=\kappa(Y,K_Y+D)+\kappa(F,K_F+E_F).$$

This is the logarithmic extension of the strongest projective additivity conjecture and includes weaker standard cases by specialization. It is known when the base is of log general type, while the general log-smooth case remains open.