I propose that we should first make a distinction between perfect justification, partially imperfect justification and completely imperfect justification. A perfect justification would be one where the justification completely rules out the possibility of the belief being false, for example, 1 + 1 = 2 completely rules out the possibilty of 1 apple + 1 apple = 2 apples being false.

Partially imperfect justification is justification that decreases the probabilty of the belief being false, but that does not completely rule it out. there are better and worse partially imperfect justifications. For example, looking at a clock and inferring that it is 12 o'clock is partially imperfect justification.

Completely imperfect justification is justification that does not affect the probability of the blief being false at all. For example, "roses are red" does not affect the probability of "John has a dog" being false at all.

Now, I'm not sure for what to do next. Based on that, we could make a distinction between perfect knowledge, partially imperfect knowledge, and completely imperfect knwoledge, or we could consider one or both of the two later as not knowledge at all.

(As I am a layman, I am aware that some philosopher I haven't read or heard about could already have proposed this idea, so inform me if it is the case)