They're Paintshop Pro native files (like .PSD is for Photoshop). You'll need either one of these apps (or whatever else may open Paintshop Pro files) to open them.
Photoshop does not open PSP files unfortunately. The only program I know for sure that opens them is Paintshop Pro; although GIMP may be able to. There is a website out there that lists many filetypes and programs which can open them/are associated with them (I think this site might be wikipedia actually...) which could be useful as well.