Syllogistic Logic with Cardinality Comparisons

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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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APA

Moss, L. S. (2016). Syllogistic Logic with Cardinality Comparisons. In Outstanding Contributions to Logic (Vol. 8, pp. 391–415). Springer. https://doi.org/10.1007/978-3-319-29300-4_18

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