A Finite Axiomatization of Conditional Independence and Inclusion Dependencies

Abstract

We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the unrestricted implication problem for inclusion, functional, and embedded multivalued dependencies in the unirelational case.

A finite axiomatization of conditional independence and inclusion dependencies

“…, x n−1 . Independence logic replaces the dependence atoms by independence atoms y⊥ x z, ✩ This article is an extended version of [17]. hence our results for independence atoms cover also the case where dependence atoms are present.…”

Axiomatizing first-order consequences in independence logic

“…Rules 3, 4, 6 and 7 preserve logical equivalence. Also note that rule 9 is analogous to the chase rule of independence and inclusion atoms in [9].…”

“…Unlike with dependence atoms, the implication problem for independence atoms is undecidable, and therefore lacks finite axiomatization [11,12]. Despite this, independence atoms have been axiomatized in [9] where completeness is obtained by using inclusion atoms and implicit existential quantification in the intermediate steps of derivations.…”

Characterizing Strongly First Order Dependencies: The Non-Jumping Relativizable Case

“…This is of considerable theoretical interest: indeed, Team Semantics may be seen as a tool to describe and classify novel fragments of Second Order Logic, an issue of great importance -and of deep connections, via Descriptive Complexity Theory, to the theory of computation -regarding which much is still not known. It is also of more direct practical interest, because of the connections between Team Semantics and Database Theory (see for instance [16,24]). Probabilistic variants of Team Semantics have recently gathered attention (see for instance [3,4,15]).…”