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        "description": "The result concerns finite set-valued relations, schema constraints and multivalued dependencies in a specified attribute context. Fourth normal form is stronger than BCNF for this redundancy. Lossless decomposition need not preserve every constraint locally or optimize queries. A property observed in one finite relation does not establish an integrity constraint for all future data. Independent related work retains credit.",
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      "statement": "# Fagin: multivalued dependencies and lossless fourth-normal-form decomposition\n\nFagin connected multivalued dependencies to lossless projection joins, defined fourth normal form beyond Boyce–Codd normal form, and proved finite-schema decomposition can reach it without information loss.\n\nA table can repeat combinations of facts even when no ordinary functional dependency detects the redundancy. Multivalued dependencies describe a different structure: for a fixed group of key fields, two groups of remaining values vary independently. Fagin proved that this tuple-swapping condition is exactly what allows the table to be reconstructed from two projections by a natural join. Fourth normal form requires nontrivial multivalued dependencies to arise from keys. Splitting a violating schema reduces the number of fields on each branch, so repeated lossless splits terminate in a fourth-normal-form family. The paper distinguishes constraints on all allowed instances from patterns in one table, and shows that a dependency’s meaning can change when other columns are projected away. It does not settle the best decomposition for every workload. Carlo Zaniolo’s independently discovered multivalued dependencies and the earlier relational/normalization framework retain their credit.\n\n## Scientific scope\n\nThe result concerns finite set-valued relations, schema constraints and multivalued dependencies in a specified attribute context. Fourth normal form is stronger than BCNF for this redundancy. Lossless decomposition need not preserve every constraint locally or optimize queries. A property observed in one finite relation does not establish an integrity constraint for all future data. Independent related work retains credit.\n\n## People and systems\n\nRonald Fagin\n\n\n\n## Original sources\n\n- [Fagin: multivalued dependencies and lossless fourth-normal-form decomposition — exact original scientific paper](https://www.comp.nus.edu.sg/~lingtw/papers/fagin.pdf)\n- [Fagin: multivalued dependencies and lossless fourth-normal-form decomposition — publisher deposit](https://api.crossref.org/works/10.1145%2F320557.320571)\n",
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