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CHARACTERIZING DOWNWARDS CLOSED, STRONGLY FIRST-ORDER, RELATIVIZABLE DEPENDENCIES

Published online by Cambridge University Press:  04 March 2019

PIETRO GALLIANI*
Affiliation:
FREE UNIVERSITY OF BOZEN-BOLZANO FACOLTÀ DI SCIENZE E TECNOLOGIE INFORMATICHE PIAZZA DOMENICANI 3, 39100 BOLZANO, ITALYE-mail: pietro.galliani@unibz.it

Abstract

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First-Order Logic is equivalent to some first-order sentence. In this work it is shown that all nontrivial dependency atoms that are strongly first order, downwards closed, and relativizable (in the sense that the relativizations of the corresponding atoms with respect to some unary predicate are expressible in terms of them) are definable in terms of constancy atoms.

Additionally, it is shown that any strongly first-order dependency is safe for any family of downwards closed dependencies, in the sense that every sentence of the logic obtained by adding to First-Order Logic both the strongly first-order dependency and the downwards closed dependencies is equivalent to some sentence of the logic obtained by adding only the downwards closed dependencies.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2019 

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CHARACTERIZING DOWNWARDS CLOSED, STRONGLY FIRST-ORDER, RELATIVIZABLE DEPENDENCIES
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