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Abstract: 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 second-order quantification to it captures precisely all Hanf-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/article/libkin00logics.html" }
Citations (may not include all citations):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, Furer et al. - 1992
66 Describing graphs: A first order approach to graph canonizat.. - Immerman, Lander - 1990
65 Modal Logic and Classical Logic (context) - van Benthem - 1985
54 and logarithmic space (context) - Etessami, successor - 1997
49 Model-theoretic methods in the study of elementary logic (context) - Hanf - 1965
49 Local properties of query languages - Dong, Libkin et al. - 2000
49 On monadic NP vs monadic co-NP (context) - Fagin, Stockmeyer et al. - 1995
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36 Generalized quantifiers and pebble games on finite structure.. (context) - Kolaitis, Vaananen - 1995
31 Notions of locality and their logical characterizations over.. - Hella, Libkin et al. - 1999
29 On winning strategies with unary quantifiers - Nurmonen - 1996
24 the restraining power of guards - Gradel - 1999
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22 Bounded Variable Logics and Counting: A Study in Finite Mode.. (context) - Otto - 1997
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17 On counting logics and local properties - Libkin - 2000
11 in and L. Wong. Unary quantifiers, transitive closure, and r.. (context) - Libk
9 Locality of order-invariant first-order formulas - Grohe, Schwentick - 2000
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1 ACM Transactions on Computational Logic (context) - Ebbinghaus, Flum et al. - 1995
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