I still don’t claim to explain exactly what knowledge is, but as a kind of minimal delimitation, following Aristotle’s usage it seems to me it should involve elements of necessity and generalization.
Then following Leibniz, I think all necessity is hypothetical, i.e., of an if-then form, rather than “categorical” or unconditional. (For Aristotle’s anticipation of this, see Aristotle on Explanation.)
That the conclusion of an Aristotelian syllogism follows from its premises, and that certain mathematical constructions necessarily have certain properties would be examples of knowledge in this sense. In both cases, the conclusion exactly follows from the agreed meaning of the content. Moreover, in both cases we have a sound material inference that is interchangeable with a valid formal inference, in that they yield equivalent results.
Most of the time, meaning-based material inferences escape formalization, and formal inferences lack definite material interpretation. My somewhat novel suggestion here is that it is just those rare cases where the same content supports both a sound material inference and a valid formal inference that seem to qualify as knowledge in Aristotle’s strict sense. (See also Opinion, Belief, Knowledge?; Everyday Belief.)
In a broader sense that Aristotle also uses, any interpretive account that is grounded in rational explanation can also be called knowledge. In this case, the grounding explanation contains elements of hypothetical necessity and generalization, but the way in which the explanation grounds the conclusion need only be reasonable, since in many cases it cannot be established as following necessarily
The Postmodern Peripatetic 