 Latin medieval theories of consequence are systematic analyses by Latin medieval  authors[1]  of the logical relations between  sentences[2],  in particular the notions of entailment and valid inference, but also the semantics of conditionals. When does a sentence B follow from a sentence A? (For example, from ‘Every human is an animal’ one may infer ‘Some animal is a human’.) What are the grounds for the relation of entailment/consequence? Are there different kinds of consequences? These and other questions were extensively debated by these authors.