can a valid argument with false premises have a true conclusion?

Yes.  Consider

Argument A

(1) No ravens are black

(2) All cats are black

(3) No ravens are cats

Argument A is valid, has false premises, and a true conclusion. Why is that, though?  Why do valid arguments “preserve truth” and not falsity? 

symbolizing arguments which employ the knowledge relation.

Kahane (enter citation) says that symbolic logic doesn’t have the resources to symbolize some arguments that are obviously valid.  For example:  Jim knows that either he’ll fly to China or to Japan. Jim knows that he won’t fly to Japan. Ergo, Jim knows that he will fly to China.

Why doesn’t the following symbolization work?

j = Jim 
K = knows that 
p = Jim will fly to China.
q = Jim will fly to Japan.

(1)  Kj(p v q) 
(2)  Kj(~q) 
(3)  Kj(p)

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