 GLP has recently been endowed with a Kripke semantics with respect to which it is complete, and has also been shown to be arithmetically complete with respect to Peano Arithmetic (see Beklemishev 2010a, 2011a). Just like for GL, the decision problem for GLP is PSPACE-complete (Shapirovsky 2008), while its closed fragment is polynomial time decidable (Pakhomov 2014).