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  1. On Second-Order Generalized Quantifiers and Finite Structures.Anders Andersson - 2002 - Annals of Pure and Applied Logic 115 (1--3):1--32.
    We consider the expressive power of second - order generalized quantifiers on finite structures, especially with respect to the types of the quantifiers. We show that on finite structures with at most binary relations, there are very powerful second - order generalized quantifiers, even of the simplest possible type. More precisely, if a logic is countable and satisfies some weak closure conditions, then there is a generalized second - order quantifier which is monadic, unary and simple, and a uniformly obtained (...)
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  • Definability of Second Order Generalized Quantifiers.Juha Kontinen - 2010 - Archive for Mathematical Logic 49 (3):379-398.
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  • Directions in Generalized Quantifier Theory.Dag Westerståhl & J. F. A. K. van Benthem - 1995 - Studia Logica 55 (3):389-419.
    We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.
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  • On the Expressive Power of Monotone Natural Language Quantifiers Over Finite Models.Jouko Väänänen & Dag Westerståhl - 2002 - Journal of Philosophical Logic 31 (4):327-358.
    We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify (...)
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  • Completeness and Interpolation of Almost‐Everywhere Quantification Over Finitely Additive Measures.João Rasga, Wafik Boulos Lotfallah & Cristina Sernadas - 2013 - Mathematical Logic Quarterly 59 (4-5):286-302.