 Could there exist a connective #′ which, when appearing outside of the scope of some specified range of operators – typically, non-Boolean connectives – behaves just like a given Boolean connective #, while behaving differently from # when occurring within the scope of one of the operators in the range in question? Understanding all of this as happening under the aegis of some particular consequence relation, on which more will be said in the following paragraph, the situation envisaged would be like this. A #′-compound would be equivalent to a #-compound of the same components, each compound having the other as a consequence by the relevant consequence relation, without being synonymous with that compound (synonymy as explained in Section  1).  The remainder of this example assumes some familiarity with the basic modal logic of “actually”. The semantics of this logic can be presented, as in the first two pages of Davies and Humberstone (1980), using models with a distinguished point (or world), with a formula Aφ evaluated as true at any point in the model just in case φ is true at the distinguished point. The generally valid formulas are then those true every point in all such models, and the generally valid sequents are those for which truth is preserved from left to right at each point in all such models. The real-world valid formulas (sequents) are those which are true (resp. truth-preserving) at the distinguished point in all models.