A Single-Type Semantics for Natural Language

Kristina Liefke (Tilburg) gives a talk at the MCMP Colloquium (26 April, 2012) titled "A Single-Type Semantics for Natural Language". Abstract: Richard Montague's Intensional Logic [2] constitutes a milestone in the project of providing a formal semantics for natural language. Its use enables the systematic translation of natural into formal language expressions and allows a mathematically rigorous account of a wide range of semantic phenomena. Despite its success, Montague's logic has, in the last decade, been subject to significant criticism [1, 3]. The latter pertains to the descriptive inadequacy of its underlying system of semantic domains, especially of the distinction between the interpretive domains of noun phrases (i.e. individuals) and sentences (i.e. propositions). To remedy this inadequacy, I develop a semantics for natural language that replaces individuals and propositions by a single type of object (hence 'single-type semantics'). In particular, I compare different single-type alternatives, identify the most suitable candidate, and show that it models a standard fragment of English.