Doubly Strongly First Order Dependencies

Galliani, Pietro

doi:10.1007/978-3-030-88853-4_4

Cited by 2 publications

(3 citation statements)

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“…Finally, in [6], a characterization was found for dependencies that are domainindependent 15 and doubly strongly first order, in the sense that they and their negation can be added to First Order Logic (separately or jointly) without increasing its expressive power.…”

Section: Definition 7 (Strongly First Order Dependencies) Let D Be a ...mentioning

confidence: 99%

“…The choice of v in the atom NE( v) is indifferent as long as it is contained in the domain of X. Thus, one could define NE as a single 0-ary dependency instead of a family of dependencies of all arities, as we do here for simplicity and uniformity 6. Theorem 1 in this work 7.…”

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confidence: 92%

“…do not increase the expressive power of First Order Logic if added to it, as per Theorem 11 of [3], 6 even though it follows easily from Proposition 1 that such an atom is not definable by any first order formula over Team Semantics. 7 Extensions of First Order Logic with Team Semantics via additional connectives have also been studied.…”

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confidence: 99%

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Strongly First Order, Domain Independent Dependencies: the Union-Closed Case

Galliani¹

2022

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Team Semantics generalizes Tarski's Semantics by defining satisfaction with respect to sets of assignments rather than with respect to single assignments. Because of this, it is possible to use Team Semantics to extend First Order Logic via new kinds of connectives or atoms -most importantly, via dependency atoms that express dependencies between different assignments. Some of these extensions are more expressive than First Order Logic proper, while others are reducible to it. In this work, I provide necessary and sufficient conditions for a dependency atom that is domain independent (in the sense that its truth or falsity in a relation does not depend on the existence in the model of elements that do not occur in the relation) and union closed (in the sense that whenever it is satisfied by all members of a family of relations it is also satisfied by their union) to be strongly first order, in the sense that the logic obtained by adding them to First Order Logic is no more expressive than First Order Logic itself.

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Section: Definition 7 (Strongly First Order Dependencies) Let D Be a ...mentioning

confidence: 99%

mentioning

confidence: 92%