Scope dominance with monotone quantifiers over finite domains

Journal of Logic, Language and Information 13 (4):385-402 (2004)
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Abstract

We characterize pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1–V–NP2. Simple numerical or set-theoretical considerations that follow from our main result are used for characterizing such relations. The variety of examples in which they hold are shown to go far beyond the familiar existential-universal type

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Citations of this work

Oppositions and opposites.Fabien Schang - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 147--173.
Scope dominance with upward monotone quantifiers.Alon Altman, Ya'Acov Peterzil & Yoad Winter - 2005 - Journal of Logic, Language and Information 14 (4):445-455.
John Buridan’s Theory of Consequence and His Octagons of Opposition.Stephen Read - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 93--110.
The Square of Opposition and Generalized Quantifiers.Duilio D'Alfonso - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 219--227.
Structures of oppositions in public announcement logic.Lorenz Demey - 2012 - In Jean-Yves Béziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. New York: Springer Verlag. pp. 313--339.

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References found in this work

Polyadic Quantifiers.Johan Van Benthem - 1989 - Linguistics and Philosophy 12 (4):437-464.
Polyadic quantifiers.Johan Benthem - 1989 - Linguistics and Philosophy 12 (4):437 - 464.
Self-commuting quantifiers.Dag Westerståhl - 1996 - Journal of Symbolic Logic 61 (1):212-224.
Scope dominance with upward monotone quantifiers.Alon Altman, Ya'Acov Peterzil & Yoad Winter - 2005 - Journal of Logic, Language and Information 14 (4):445-455.
Scopeless quantifiers and operators.Thomas Ede Zimmermann - 1993 - Journal of Philosophical Logic 22 (5):545 - 561.

View all 7 references / Add more references