Relational Domains and the Interpretation of Reciprocals

Expressions like know and stand on are standardly analyzed as denoting binary relations between entities. Sentence (1) can be paraphrased by requiring that every element of the set {Mary,Sue,Jane} is in the know relation with every other element of this set. By contrast, in sentence (2) an analogous interpretation is highly unlikely. We describe the contrast in Figure 1, modeling binary relations using directed graphs (Tutte 2001). In sentence (1) the know relation is required to constitute a complete directed graph (possibly with loops) over the three entities for Mary, Sue and Jane. Sentence (2) is true when the graph described by the stand on relation is not complete but constitutes a directed path. Similar variations in the interpretation of reciprocal sentences have repeatedly been demonstrated in the literature.1