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Conditional Independence on Semiring Relations

Author Miika Hannula

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Miika Hannula
  • University of Helsinki, Finland

Funding

  • Hannula, Miika: The author has been supported by the ERC grant 101020762.

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Miika Hannula. Conditional Independence on Semiring Relations. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICDT.2024.20

Abstract

Conditional independence plays a foundational role in database theory, probability theory, information theory, and graphical models. In databases, a notion similar to conditional independence, known as the (embedded) multivalued dependency, appears in database normalization. Many properties of conditional independence are shared across various domains, and to some extent these commonalities can be studied through a measure-theoretic approach. The present paper proposes an alternative approach via semiring relations, defined by extending database relations with tuple annotations from some commutative semiring. Integrating various interpretations of conditional independence in this context, we investigate how the choice of the underlying semiring impacts the corresponding axiomatic and decomposition properties. We specifically identify positivity and multiplicative cancellativity as the key semiring properties that enable extending results from the relational context to the broader semiring framework. Additionally, we explore the relationships between different conditional independence notions through model theory.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database theory
Keywords
  • semiring
  • conditional independence
  • functional dependency
  • decomposition
  • axiom

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