Linearizing sets: each other

It is has been well known since Fiengo and Lasnik (1973) and Langendoen (1978) that each other presents a high degree of contextual variability. In a tradition that goes back to Langendoen (1978) and later to Dalrymple et al. (1998), theoreticians have tried to list different truth conditions and to establish a criterion for determining which one holds in which particular context. Along the lines of a competitive tradition going back to Fiengo and Lasnik (1973) and Heim (Lasnik and May), authors have tried capture the contextual variation of each other by a unique rule. Along this line of thought, Beck (2001) has recently provided convincing arguments for reducing the possible known and attested meanings to four basic interpretations three of which can be analyzed in the light of a unique rule. These interpretations are, ordered by strength: strong reciprocity, weak reciprocity, partitioned reciprocity, and linear orderings. The last configuration, illustrated in (1), however, escapes the unifying account and seems hardly reconcilable with strong and weak reciprocity.