| Issue |
RAIRO-Theor. Inf. Appl.
Volume 42, Number 1, January-March 2008
A nonstandard spirit among computer scientists:a tribute to Serge Grigorieff at the occasion of his 60th birthday
|
|
|---|---|---|
| Page(s) | 121 - 135 | |
| DOI | https://doi.org/10.1051/ita:2007047 | |
| Published online | 18 January 2008 | |
Deciding whether a relation defined in Presburger logic can be defined in weaker logics
LIAFA, Université de Paris 7,
2 place Jussieu, 75251 Paris Cedex 05; cc@liafa.jussieu.fr
We consider logics on
and 
which are weaker than
Presburger arithmetic and
we settle the following decision
problem: given a k-ary
relation on and
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.
Mathematics Subject Classification: 03B10 / 68Q70
Key words: Presburger arithmetic / first order logic / decidability
© EDP Sciences, 2007
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