SYLLOGISTIC LOGIC WITH CARDINALITY COMPARISONS, ON INFINITE SETS
LAWRENCE S. MOSS, Selçuk Topal · The Review of Symbolic Logic · 2018
Abstract This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: Allxareyand Somexarey, There are at least as manyxasy, and There are morexthany. Herexandyrange over subsets (not elements) of a giveninfiniteset. Moreover,xandymay appear complemented (i.e., as $\bar{x}$ and $\bar{y}$ ), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness/completeness theorem. There are efficient algorithms for proof search and model construction.