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The problem of logical omniscience breaks down to the problems of the closure of knowledge under implication and of the distribution of knowledge over implication. In late medieval scholasticism these two related issues were engaged in various genres, in particular in general analysis of validity, games of obligationes, solution to self-referential antinomies and semantics of terms. The present study analyses the corpus of fourteenth-century texts with some overreaches to the subsequent two centuries, attempting to cover representatives of both the “British” and the “Continental” tradition. With some degree of simplification, this results in a range of four basic positions: 1. knowledge is closed under “analytic entailment” (Buridan), 2. knowledge distributes over implication (Heytesbury), 3. knowledge distributes over implication provided that its consequent’s truth is being taken into consideration (Peter of Mantua), 4. knowledge does not distribute overimplication (Wyclif).