This paper provides a semantics for input/input output logic based on formal concept analysis. The central result shows that an input/output logic axiomatised by a relation R is the same as the logic induced by deriving pairs from the concept lattice generated by R using a ∧- and ∨-classical Scott consequence relation. This correspondence offers powerful analytical techniques for classifying, visualising and analysing input/output relations, revealing implicit hierarchical structure and/or natural clusterings and dependencies. The application of all formal developments are illustrated by a worked example towards the end.