Abstract
This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So in addition to assertions like All x are y and Some x are y, we also have There are at least as many x as y, and There are more x than y. Our work also allows all nouns to be complemented. We thus obtain sentences equivalent to No x are y and At least half of the universe are x. We work on finite models exclusively. We formulate a syllogistic logic for our language. The main result is a soundness/completeness theorem. The logic has a rule of ex falso quodlibet, and reductio ad absurdum is admissible. There are efficient algorithms for proof search and model construction, and the logic has been implemented.
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I thank anonymous reviewers for their comments and corrections to this paper.
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Moss, L.S. (2016). Syllogistic Logic with Cardinality Comparisons. In: Bimbó, K. (eds) J. Michael Dunn on Information Based Logics. Outstanding Contributions to Logic, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-29300-4_18
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DOI: https://doi.org/10.1007/978-3-319-29300-4_18
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