  This paper presents a sequent calculus and a dual domain semantics for a
theory of definite descriptions in which these expressions are formalised in
the context of complete sentences by a binary quantifier $I$. $I$ forms a
formula from two formulas. $Ix[F, G]$ means `The $F$ is $G$'. This approach has
the advantage of incorporating scope distinctions directly into the notation.
Cut elimination is proved for a system of classical positive free logic with
$I$ and it is shown to be sound and complete for the semantics. The system has
a number of novel features and is briefly compared to the usual approach of
formalising `the $F$' by a term forming operator. It does not coincide with
Hintikka's and Lambert's preferred theories, but the divergence is
well-motivated and attractive.
