  Multi-word expressions, verb-particle constructions, idiomatically combining
phrases, and phrasal idioms have something in common: not all of their elements
contribute to the argument structure of the predicate implicated by the
expression.
  Radically lexicalized theories of grammar that avoid string-, term-, logical
form-, and tree-writing, and categorial grammars that avoid wrap operation,
make predictions about the categories involved in verb-particles and phrasal
idioms. They may require singleton types, which can only substitute for one
value, not just for one kind of value. These types are asymmetric: they can be
arguments only. They also narrowly constrain the kind of semantic value that
can correspond to such syntactic categories. Idiomatically combining phrases do
not subcategorize for singleton types, and they exploit another locally
computable and compositional property of a correspondence, that every syntactic
expression can project its head word. Such MWEs can be seen as empirically
realized categorial possibilities, rather than lacuna in a theory of
lexicalizable syntactic categories.
