Hm. Most of the limited amount I ever knew about this I've forgotten atm, but in the face of general misunderstanding I'm going to chance my arm on the theory that I have a >50% chance of making things better rather than worse. Here goes.

Usually, in philosophical logic, you don't use 3VL or any multi-valued logic to deal with something being unknown. If you don't know whether the proposition P is true or false, and so you don't want to assert either that it is true or that it is false, then you do this simply by not asserting or implying P while also not asserting or implying ~P. If you want a logic in which you can actually make the statement "it is unknown whether P or ~P" (or more precisely, a logic in which you can capture the structure of that statement: you could always just define the proposition Q to mean "it is unknown whether P or ~P", but that probably doesn't get you anything useful) then you'd probably use some variation on modal logic https://en.wikipedia.org/wiki/Epistemic_modal_logic , not a 3VL. What logicians actually normally use 3VLs for is to (try to) deal with truth value gaps or gluts. In a logic with truth-value gluts P can be both true and false at the same time. In a logic with truth-value gaps P can be neither true nor false, at the same time. I know right? (Intuitionistic logic is something a bit different again.)

The reason that computer systems like SQL use a third truth-value which sometimes(!) means 'unknown', is, to summarise, because the way those systems handle truth and implication is a garbage fire.

Oh, you'd be in good company, if for (likely) somewhat different reasons. Google up 'C.J. Date' and '3VL' for some expert ranting on the topic.