The LFP Framework is an extension of the Harper–Honsell–Plotkin’s Edinburgh Logical Framework LF with external
predicates, hence the name Open Logical Framework. This is accomplished by defining lock type constructors, which are a
sort of -modality constructors, releasing their argument under the condition that a possibly external predicate is satisfied
on an appropriate typed judgement. Lock types are defined using the standard pattern of constructive type theory, i.e. via
introduction, elimination and equality rules. Using LFP , one can factor out the complexity of encoding specific features of
logical systems, which would otherwise be awkwardly encoded in LF, e.g. side-conditions in the application of rules in Modal
Logics, and sub-structural rules, as in non-commutative Linear Logic. The idea of LFP is that these conditions need only
to be specified, while their verification can be delegated to an external proof engine, in the style of the Poincaré Principle
or Deduction Modulo. Indeed such paradigms can be adequately formalized in LFP . We investigate and characterize the
meta-theoretical properties of the calculus underpinning LFP : strong normalization, confluence and subject reduction. This
latter property holds under the assumption that the predicates are well-behaved, i.e. closed under weakening, permutation,
substitution and reduction in the arguments. Moreover, we provide a canonical presentation of LFP , based on a suitable
extension of the notion of βη-long normal form, allowing for smooth formulations of adequacy statements.