THE LOGIC OF COMPARATIVE CARDINALITY
Yifeng Ding, Matthew Harrison‐Trainor, Wesley H. Holliday
Abstract
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.
Topics & Concepts
Cardinality (data modeling)Intersection (aeronautics)Boolean algebraMathematicsComputer scienceTheoretical computer scienceDiscrete mathematicsAlgebra over a fieldPure mathematicsData miningEngineeringAerospace engineeringComputability, Logic, AI AlgorithmsAdvanced Algebra and LogicMathematical and Theoretical Analysis