We introduce a generic notion of categorical propositional logic and provide a construction of a preorder-enriched institution out of such a logic, following the Curry-Howard-Tait paradigm. The logics are speci ed as theories of a meta-logic within the logical framework LF such that institution comorphisms are obtained from theory morphisms of the meta-logic. We prove several logic-independent results including soundness and completeness theorems and instantiate our framework with a number of examples: classical, intuitionistic,linear and modal propositional logic.