Abstract A novel contextual logic is presented that combines features of both multi-context systems and logics of context. Broadly, contextual logics are those with a formal notion of context — knowledge that is true only under specific assumptions. Multi-context systems use discrete logistic systems as individual contexts, related by meta-level rules, whereas logics of context partition a single knowledge base into contexts, related using object-level rules. The contextual logic presented here is strongly-local, in that knowledge and inference is discrete for individual contexts, but which are nevertheless part of a single logistic system that relates contexts at the objectlevel, so combining advantages of both. A deductive system of contextual inference and a possibleworlds based semantics is given, with formal results including soundness and completeness, and a number of properties are examined.