Pre-final version

International audienceReciprocal sentences display a variety of interpretations, including 'strong reci-procity'. In this interpretation, every element of the reference set participates with every other element in the same set in the relation provided by the predicate. Another interpretation is 'inclusive alternative orderings'. In this interpretation, every element in the reference set participates with some other member in the relation provided by the predicate either as the first or second argument. Current reciprocal theories cannot explain why some sentences that satisfy these truth conditions are in fact false and infelicitous, such as '#my mother and I gave birth to each other'. This paper defends the view that strong reciprocity has a privileged status. Its core insight is that reciprocal sentences are true if they describe a relation that is either actually or possibly strong reciprocal over the reference set, insofar as the possibilities are reasonable. The new truth conditions are cast in a branching time framework (Thomason, 1984), in which a new notion of reasonability is defined (vs. inertia, Dowty, 1979; see also Landman, 1992). On the empirical side, we show that when the relation is asymmetric, it must be non-permanent for the reciprocal each other-sentence to be true. We also note that, in some cases, the relation is asymmetric and non-permanent, but the each other-sentences are false. We explain these facts by introducing a new notion of 'decidedness' that we define in modal terms. We explain that the relation should not be decided for the reciprocal sentence to be true. We also provide a new definition for asymmetry and (non-)permanency in the modal framework and explain how asymmetry, (non-)decidedness and (non-)permanency interact, ensuring large empirical coverage