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A Graph-theoretic Method to Define any Boolean Operation on Partitions

Ellerman, David (2019) A Graph-theoretic Method to Define any Boolean Operation on Partitions. [Preprint]

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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
Creators:
CreatorsEmailORCID
Ellerman, Daviddavid@ellerman.org0000-0002-5718-618X
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: http://philsci-archive.pitt.edu/id/eprint/16106

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