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Deciding whether a relation defined inPresburger logic can be defined in weaker logics

Published online by Cambridge University Press:  18 January 2008

Christian Choffrut*
Affiliation:
LIAFA, Université de Paris 7, 2 place Jussieu, 75251 Paris Cedex 05; cc@liafa.jussieu.fr
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Abstract

We consider logics on $\mathbb{Z}$ and $\mathbb{N}$ which are weaker than Presburger arithmetic and we settle the following decision problem: given a k-ary relation on $\mathbb{Z}$ and $\mathbb{N}$ which are first order definable in Presburger arithmetic, are they definable in these weaker logics? These logics, intuitively, are obtained by considering modulo and threshold counting predicates for differences of two variables.

Type
Research Article
Copyright
© EDP Sciences, 2007

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References

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