The immediate response was that within the theorem proving community the paradigm for the distinction is explicit, namely, having a formal proof of a claim instead of just making the claim. Later discussion in the seminar of archival functions introduced another aspect of distinguishing knowledge, namely recordkeeping. Records management aims at supporting inferences based upon existence of records.
Remark
A good segue which I neglected to think of at the time would have been, in the domain of computer supported logic, to pose the further question of how does one know one has a formal proof (ignoring here the establishment of correctness of the logic).
As users of applied logics we may be inclined to think that making a criterion of proof effective, and implementing a computer system to apply it, is enough to answer the question. But in fact our knowledge that we have formal proofs is typically not acheived by applying these procedures whenever knowledge is attempted; the bulk of such knowledge is actually based upon reference to records that such knowledge-establishing procedures have been applied in specific cases before.
Thus, weaknesses in recordkeeping are actual liabilities in computer supported logic. Making such recordkeeping methods reliable support for such claims to knowledge is the purview of archival science.
I hope that in seminar these complementary aspects of distinguishing knowledge were brought out, but I don't think I showed the connection to be as tight as this example would have.