In this article I will argue that clefts differ in more than simply their i
nformation structure from their noncleft counterparts. Clefts are construct
ions in their own right, whose grammatical features convey specific represe
ntational semantics. I will focus on the two main coded relations in cleft
constructions: the one expressed by the matrix clause and the anaphoric I e
lation between the complement of the matrix clause and the relative clause.
I will indicate in which ways these have not been described satisfactorily
in the literature so far and will propose an alternative description. The
different matrix clauses of clefts are specific subtypes of identifying, ex
istential, and possessive clauses, which all impose a specific "quantificat
ional" value on their complement: they express exhaustive specification of
a set, enumeration, or cardinal quantification of instances. The relative c
lause takes this specifying, enumerating, or cardinally measured complement
as antecedent and incorporates it in a value-variable relation. In this wa
y, I will argue, the different types of clefts, viz. it clefts, there cleft
s, and possessive clefts, can be given an integrated semantic description.