 What is the point of considering such two-dimensional isotopes of Boolean disjunction? Fusco’s idea is the following. Arguably, people have thought that the correct treatment of inclusive “or” in English is given by (Boolean) “∨”, once they have learned to diagnose as pragmatic distraction any apparent anomalies, because this simple connective with its truth-functional semantics captures the way “or” behaves when it appears unembedded (or only ‘Booleanly’ embedded). The presumption has then been that any residual anomalies arising from problematic embeddings will be eventually also then be explained away pragmatically. But what if we had on our hands a two-dimensional isotope of ∨ that was specially hand-crafted to deal with these anomalies, such as Fusco’s or? The unembedded behaviour of ∨ and or, in view of the diagonal equivalence of compounds formed using the two disjunctions, would be the same, so or-disjunction would have all the benefits of Boolean disjunction without the drawback of not faring very satisfactorily when appearing in the scope of certain intensional operators. On this matter of agreement in logical behaviour when unembedded, consider, for example, the introduction and elimination rules in a natural deduction system. What they introduce or eliminate is the main connective of a formula, so they would not differ in their intuitive acceptability in the case of “or” whether this was rendered as Boolean disjunction ∨ or as Fusco’s two-dimensional or  connective.[52]  More generally, the conditions defining ∨-classicality (indeed #-classicality for any #) of consequence relations or generalized consequence relations pertain only to unembedded occurrences of ∨ (or more generally of #). In the case of Fusco (2015), the obligation operator O is interpreted by universal quantification over suitably accessible points with the relata of this relation being the worlds of local evaluation rather than the world taken as the actual world, which remains the same, so while p or q is a diagonal (though not a general) consequence of p, O(p or q) is not a diagonal consequence of  Op.[53]  Putting it very informally, this is because from the perspective of some world of evaluation, w, with w itself considered as actual (since we are working the diagonal case), every world deontically accessible to w, qua world of evaluation, may be a p-world, whereas at w if what is true is q but not p, then what is required for the truth at w of O(p or q) is that all the accessible worlds be q-worlds, since in moving out to the w-accessible worlds we are not changing the status of w as the world playing the actual world role. (We are in the ‘middle disjunct’ case of (2) with this example.) This illustrates how Fusco has arranged matters so that p or q and p ∨ q end up exhibiting the same behaviour when unembedded but differing behaviour when embedded – in the present instance, in the scope of the obligation operator. The story with the permissibility operator, written as may or M in Fusco (2015), and not there treated as dual to O, is more complicated, so the interested reader is referred to that discussion for the details as well as the motivation behind the choice of or in this setting. For present purposes, the main point to stress is the general strategy of using the two-dimensional semantics to model differences in ingredient sense compatible with a given assertoric content.