  We study the cohomology rings of snc log symplectic pairs $(X,Y)$ which have
log symplectic forms of pure weight. We show that under a certain natural
condition, the cohomology ring of $X \setminus Y$ exhibits the curious hard
Lefschetz property. Analogous results are shown to hold for limit mixed Hodge
structures associated to good degenerations of projective irreducible
holomorphic symplectic manifolds. We provide several examples of log symplectic
pairs of pure weight including a class of cluster-type varieties, and examples
coming from the work of Feigin and Odesski. We show that the components of the
central fiber of good degenerations of projective irreducible holomorphic
symplectic manifolds produce log symplectic pairs.
