Galois Connections in Categorial Type Logic

The introduction of unary connectives has proved to be an important addition to the categorial vocabulary. The connectives considered so far are order-preserving; in this paper instead, we consider the addition of order-reversing, Galois connected operators. In §2 we do the basic model-theoretic and proof-theoretic groundwork. In §3 we use the expressive power of the Galois connected operators to restrict the scopal possibilities of generalized quantifier expressions, and to describe a typology of polarity items.