Abstract
The partitions of a given set stand in a well known one-to-onecorrespondence with the equivalence relations on that set. We askwhether anything analogous to partitions can be found which correspondin a like manner to the similarity relations (reflexive, symmetricrelations) on a set, and show that (what we call) decompositions – of acertain kind – play this role. A key ingredient in the discussion is akind of closure relation (analogous to the consequence relationsconsidered in formal logic) having nothing especially to do with thesimilarity issue, and we devote a final section to highlighting some ofits properties.
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Hazen, A., Humberstone, L. Similarity Relations and the Preservation of Solidity. Journal of Logic, Language and Information 13, 25–46 (2004). https://doi.org/10.1023/A:1026132413897
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DOI: https://doi.org/10.1023/A:1026132413897