Ellerman, David (2019) A Graph-theoretic Method to Define any Boolean Operation on Partitions. [Preprint]
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Official URL: https://adam-journal.eu/index.php/ADAM/article/vie...
Abstract
The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.
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| Item Type: | Preprint | ||||||
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| Keywords: | logic of partitions, Boolean logic of subsets, Boolean operations | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic | ||||||
| Depositing User: | David Ellerman | ||||||
| Date Deposited: | 12 Jun 2019 19:24 | ||||||
| Last Modified: | 12 Jun 2019 19:24 | ||||||
| Item ID: | 16106 | ||||||
| Official URL: | https://adam-journal.eu/index.php/ADAM/article/vie... | ||||||
| DOI or Unique Handle: | 10.26493/2590-9770.1259.9d5 | ||||||
| Subjects: | Specific Sciences > Mathematics > Logic | ||||||
| Date: | 10 June 2019 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/16106 |
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