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The logic of comparative cardinality
Journal of Symbolic Logic 85 (3):972-1005 (2020)
Abstract
This paper investigates the principles that one must add to Boolean algebra to capture reasoning not only about intersection, union, and complementation of sets, but also about the relative size of sets. We completely axiomatize such reasoning under the Cantorian definition of relative size in terms of injections.Author Profiles
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2020-01-15
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6 months
9 (#302,300)
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Citations of this work
Probing the quantitative–qualitative divide in probabilistic reasoning.Duligur Ibeling, Thomas Icard, Krzysztof Mierzewski & Milan Mossé - forthcoming - Annals of Pure and Applied Logic.
Generalized Quantifiers Meet Modal Neighborhood Semantics.Dag Westerståhl & Johan van Benthem - 2021 - In Judit Madarász & Gergely Székely (eds.), Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic. Springer. pp. 187-206.
References found in this work
Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor’s Theory of Infinite Number Inevitable?Paolo Mancosu - 2009 - Review of Symbolic Logic 2 (4):612-646.
Qualitative probability as an intensional logic.Peter Gärdenfors - 1975 - Journal of Philosophical Logic 4 (2):171 - 185.
Syllogistic Logic with Cardinality Comparisons, on Infinite Sets.Lawrence S. Moss & Selçuk Topal - 2020 - Review of Symbolic Logic 13 (1):1-22.
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