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On the locality of arb-invariant first-order logic with modulo counting quantifiers Harwath, Frederik Schweikardt, Nicole finite model theory Gaifman and Hanf locality first-order logic with modulo counting quantifiers order-invariant and arb-invariant formulas lower We study Gaifman and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MODp, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas. This paper gives a detailed picture of locality and non-locality properties of arb-invariant FO+MODp. For example, on the class of all finite structures, for any p >= 2, arb-invariant FO+MODp is neither Hanf nor Gaifman local with respect to a sublinear locality radius. However, in case that p is an odd prime power, it is weakly Gaifman local with a polylogarithmic locality radius. And when restricting attention to the class of string structures, for odd prime powers p, arb-invariant FO+MODp is both Hanf and Gaifman local with a polylogarithmic locality radius. Our negative results build on examples of order-invariant FO+MODp formulas presented in Niemistö's PhD thesis. Our positive results make use of the close connection between FO+MODp and Boolean circuits built from NOT-gates and AND-, OR-, and MODp-gates of arbitrary fan-in. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Frederik Harwath and Nicole Schweikardt 2013 Is Part Of LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2013.363 urn:nbn:de:0030-drops-42086 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.363 eng https://creativecommons.org/licenses/by/3.0/legalcode