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Abstract: Well-known theorems of Hanf and Gaifman establishing locality... In this paper, we give logical characterizations of local properties behind Hanf's and Gaifman's theorems. We first deal with an infinitary logic with counting terms and quantifiers that is known to capture Hanf-locality on structures of bounded valence. We show that testing isomorphism of neighborhoods can be added to it without violating Hanf-locality, while increasing its expressive power. We then show that adding local... (Update)
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BibTeX entry: (Update)
@article{ libkin01logics,
author = "Leonid Libkin",
title = "Logics capturing local properties",
journal = "{ACM} Transactions on Computational Logic",
volume = "2",
number = "1",
pages = "135--153",
year = "2001",
url = "citeseer.ist.psu.edu/libkin01logics.html" }
Citations (may not include all citations):294 Finite Model Theory (context) - Ebbinghaus, Flum - 1995
116 On uniformity within NC - Barrington, Immerman et al. - 1990
116 On local and non-local properties (context) - Gaifman - 1982
110 Descriptive Complexity (context) - Immerman - 1999
98 On optimal lower bound on the number of variables for graph .. - Cai, urer et al. - 1992
49 Model-theoretic methods in the study of elementary logic (context) - Hanf - 1965
49 On monadic NP vs monadic co-NP (context) - Fagin, Stockmeyer et al. - 1995
49 Local properties of query languages - Dong, Libkin et al. - 2000 ACM DBLP
40 the restraining power of guards - adel, On - 1999
31 Notions of locality and their logical characterizations over.. - Hella, Libkin et al.
24 Logics with aggregate operators - Hella, Libkin et al. ACM DBLP
22 Bounded Variable Logics and Counting: A Study in Finite Mode.. (context) - Otto - 1997
21 Logical hierarchies in PTIME (context) - Hella - 1996 ACM DBLP
20 Expressive power of unary counters - Benedikt, Keisler - 1997 ACM DBLP
17 On counting logics and local properties - Libkin - 2000 ACM DBLP
14 Describing graphs: A rst order approach to graph canonizatio.. (context) - Immerman, Lander - 1990
9 Generalized quantiers and pebble games on nite structures (context) - Ph, an - 1995
5 Locality of order-invariant rst-order formulas (context) - Grohe, Schwentick - 2000
3 On winning strategies with unary quantiers (context) - Nurmonen - 1996
2 Local normal forms for rst-order logic with applications to .. (context) - Th - 1998
1 Metanite model theory (context) - adel, Gurevich - 1998
1 Counting quantiers (context) - Etessami - 1997
1 Unary quantiers (context) - Libkin, Wong - 1998
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