Proof-Theoretic Reconstruction of Generalized Quantifiers
Nissim Francez, Gilad Ben-Avi · Journal of Semantics · 2014
The article presents a proof-theoretic semantic (PTS) analysis of determiners. Its main contribution is the introduction of a proof-theoretical substitute for noun-phrase and determiner meanings, thereby replacing the traditional model-theoretical appeal to generalized quantifiers, and proving conservativity from a proof-theoretic point of view. The article proposes a definition of negative determiners, leading naturally to a bilateral PTS for them. The main technical tool used is a proof-theoretic interpret-ation of semantic types, replacing the traditional Montagovian model-theoretic interpretation. 1