Similarity relations and the preservation of solidity

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.
Keywords closure operators  partitions  proximity relations  similarity  truth functions
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DOI 10.1023/A:1026132413897
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A. J. Cotnoir (2013). Parts as Counterparts. Thought: A Journal of Philosophy 2 (3):228-241.
Hannes Leitgeb (2007). A New Analysis of Quasianalysis. Journal of Philosophical Logic 36 (2):181-226.
Thomas Mormann (2009). New Work for Carnap's Quasi-Analysis. Journal of Philosophical Logic 38 (3):249-282.
Thomas Mormann (2009). New Work for Carnap’s Quasi-Analysis. Journal of Philosophical Logic 38 (3):249-282.

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