Abstract
We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections between independence in database theory and stochastic independence. As indeed, in light of the aforementioned reduction and recent work of Ben-Yaacov (Isr. J. Math. 194(2):957–1012, 2013), the former case of independence can be seen as the discrete version of the latter.
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The research of the second author was supported by the Finnish Academy of Science and Letters (Vilho, Yrjö and Kalle Väisälä foundation). The authors would like to thank the referee for suggesting a simpler and slightly more general proof of the main theorem. The authors would also like to thank John Baldwin and Jouko Väänänen for useful suggestions and discussions related to this paper.
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Hyttinen, T., Paolini, G. Reduction of database independence to dividing in atomless Boolean algebras. Arch. Math. Logic 55, 505–518 (2016). https://doi.org/10.1007/s00153-016-0477-8
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DOI: https://doi.org/10.1007/s00153-016-0477-8