Presents a series of generalizations of distributivity operators across a type hierarchy, in order to account for collective-distributive ambiguities for non-subject arguments.

The grammatical constraints on anaphoric binding, known as binding principles, are observed to form a classical square of oppositions. These constraints are then analysed as the effect of phase quantifiers over reference markers in grammatical obliqueness hierarchies, and the resulting phase quantifiers are shown to be organised in a square of logical duality. The impact of this result on the distinction between quantificational and referential nominals as well as on the logical foundations of the semantics of nominals in general is (...) discussed. (shrink)