Abstract

Reciprocal sentences display a variety of interpretations, ranging from ‘strong reciprocity’ to ‘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 fully explain why some sentences that satisfy these truth conditions are in fact false and unacceptable, such as ‘#the boys are taller than each other’ or ‘#my mother and I procreated each other.’ The core insight of the paper 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. A branching time framework is used, in which a notion of reasonability is defined. We focus on permanent relations, for which we provide a new definition in modal terms. We show that whenever the relation is asymmetric and permanent, each other-sentences are unacceptable. We consider cases in which the relation is asymmetric and non-permanent and the each other-sentences are also unacceptable. We introduce a new modal notion of decidedness, and prove that for asymmetric relations, permanency entails decidedness. Showing how (a)symmetry, (non-)decidedness and (non-)permanency interact and proving that the truth of each other-sentences requires the relation to be either non-asymmetric or non-decided, we ensure a large and previously unattained empirical coverage