The Smithy mentions a forthcoming book, Later Medieval Metaphysics
Ontology, Language, and Logic, and quotes an author of one of its essays, Terence Parsons, for his definition of medieval logic:

The first task is to decide what to count as medieval logic. Medieval logic consists of centuries of work by some very smart people working in a difficult area. I will be libertine about what is included in medieval logic. If any medieval logician ever said it, and if it is worthwhile, it is part of medieval logic.

It is rather circular, if a medieval logician is someone who writes about medieval logic. But Parsons probably refers to commentaries on the texts of Aristotlte and so on instead.