You don't need any articles here. You should put the determiner "any" before the noun "logic". I don't see any logic in your words.

It is better to say "I don't see THE logic in your argument." You could also say "I don't see ANY logic in your argument." PS Use of "your words," although not wrong, may not be as natural/logical as "your argument."

"I don't see THE logic in your words." This is still sounds a little awkward though. A better way to say this is "I don't see your logic" or "I don't see the logic in your argument/statement." We usually don't think of about the logic of words (words are just things/objects. Logic is something in ideas or thoughts.)