  We introduce BPDL, a combination of propositional dynamic logic PDL with the
basic four-valued modal logic BK studied by Odintsov and Wansing (`Modal logics
with Belnapian truth values', J. Appl. Non-Class. Log. 20, 279--301 (2010)). We
modify the standard arguments based on canonical models and filtration to suit
the four-valued context and prove weak completeness and decidability of BPDL.
