Proof-Theory and Semantics for a Theory of Definite Descriptions

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