We study generalized quantifiers on finite structures. With every function f : ! ! ! we associate a quantifier Qf by lettingQfx' say “there are at least f(n) elementsx satisfying', where n is the… (More)

A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including ‘donkey… (More)

We characterize the generalized quantifiers Q which satisfy the scheme QxQyφ ↔ QyQxφ, the so-called self-commuting quantifiers, or quantifiers with the Fubini property.

A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a… (More)

Tarski’s definition of logical consequence for an interpreted language rests on the distinction between extra-logical symbols, whose interpretation is allowed to vary across models, and logical… (More)

1. Introduction The study of generalized quantifiers is by now an old and respectable field of logic. With the pioneering work of Mostowski and Lindström in the fifties and sixties, quantifiers… (More)

The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside… (More)