The interpretation of reciprocal expressions (each other, one another) exhibits a remarkably wide variation, which is affected in intricate ways by the predicate in the scope of the reciprocal. For example, sentence (1) entails that each person in the group likes every other person in the group, while sentences (2) and (3) do not entail an analogous claim:
(1) These three people like each other.
(2) The three planks are stacked on top of each other.
(3) The 3rd grade students gave each other measles.
Sentence (2) does not require that each plank is stacked on top of each of the other planks - an impossible configuration - but rather only requires that the planks are arranged into one stack. Similarly, sentence (3) does not require that each student give each of the other students measles - which is impossible since no one can get measles from more than one person. In an attempt to explain this phenomenon, Dalrymple et al. (1998) introduced the
Strongest Meaning Hypothesis (SMH). According to this principle, the reading associated with the reciprocal in a given sentence is the strongest available reading which is consistent with relevant information supplied by the context. Dalrymple et al. postulate an array of reciprocal meanings which the SMH has to choose from, independently of the SMH itself and the semantic properties of predicates. In this talk we propose a new system for predicting the interpretation of reciprocals in a given sentence. In this system, the SMH is implemented as a mapping from semantic restrictions on the predicate's denotation into the interpretation of the reciprocal, with no independent assumptions about available reciprocal meanings. We present methods to construct a test for the availability of a reciprocal meaning, or otherwise to prove that a speciffic meaning is not available for reciprocals. These methods are then used to analyze two previously suggested reciprocal meanings.