Syllogistic Logic with “Most”
This paper presents a sound and complete proof system for the logical system whose sentences are of the form AllXareY, Some X are Y and Most X are Y, where we interpret these sentences on finite models, with the meaning of “most” being “strictly more than half.” Our proof system is syllogistic; there are no individual variables.
We thank the many people who have discussed this topic with us, including Elizabeth Kammer, Tri Lai, Ian Pratt-Hartmann, Selçuk Topal, Chloe Urbanski, Erik Wennstrom, and Sam Ziegler.
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