Deciding whether a relation defined in Presburger logic can be defined in weaker logics
RAIRO - Theoretical Informatics and Applications (2008)
- Volume: 42, Issue: 1, page 121-135
- ISSN: 0988-3754
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topChoffrut, Christian. "Deciding whether a relation defined in Presburger logic can be defined in weaker logics." RAIRO - Theoretical Informatics and Applications 42.1 (2008): 121-135. <http://eudml.org/doc/250349>.
@article{Choffrut2008,
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.
},
author = {Choffrut, Christian},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Presburger arithmetic; first order logic; decidability; first-order logic},
language = {eng},
month = {1},
number = {1},
pages = {121-135},
publisher = {EDP Sciences},
title = {Deciding whether a relation defined in Presburger logic can be defined in weaker logics},
url = {http://eudml.org/doc/250349},
volume = {42},
year = {2008},
}
TY - JOUR
AU - Choffrut, Christian
TI - Deciding whether a relation defined in Presburger logic can be defined in weaker logics
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/1//
PB - EDP Sciences
VL - 42
IS - 1
SP - 121
EP - 135
AB -
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.
LA - eng
KW - Presburger arithmetic; first order logic; decidability; first-order logic
UR - http://eudml.org/doc/250349
ER -
References
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