The SEP article on justification logic opens by saying:
You may say, “I know that Abraham Lincoln was a tall man. ” In turn you may be asked how you know. You would almost certainly not reply semantically, Hintikka-style, that Abraham Lincoln was tall in all situations compatible with your knowledge. Instead you would more likely say, “I read about Abraham Lincoln’s height in several books, and I have seen photographs of him next to other people. ” One certifies knowledge by providing a reason, a justification. Hintikka semantics captures knowledge as true belief. Justification logics supply the missing third component of Plato’s characterization of knowledge as justified true belief.
The SEP article you mention addresses acceptance of the JTB = K account in modern times by bringing up the Gettier problem, which is that we have come to see that it seems as if there are cases where we have true beliefs with justifications that don't satisfy the negative background condition of a non-accidental connection between the justifications and the truths of such beliefs. So then do some philosophers, again as mentioned in that same article and such as Timothy Williamson, say that the concept of knowledge can't really be exhaustively broken into more fundamental components (see also this IEP entry). One way they put it is that K = E, where "E" stands for evidence, and so instead of knowledge being evident true belief, knowledge is the evidence that can be had for true beliefs.
Incidentally, in epistemic logic, some analysts suspend the factivity of knowledge (KP → P) in constructing various systems (one motive for this suspension being in approaches to Fitch's paradox of knowability), so it stands to possible reason that other systems might be constructed in which the justification condition is suspended, too, that K = TB perhaps, then, there (to refer again to the SEP article you provided a link for, they call this "lightweight knowledge").
Further reading (select examples):
- "Williamson on Knowledge and Evidence" (a critical, but appreciative, analysis from Alvin Goldman)
- Sackris and Beebe[??], "Is Justification Necessary for Knowledge?"
- Eliminative Materialism (another SEP entry, about a theory according to which beliefs do not exist, which would imply that, if K = some X still, yet this X will not include B!)