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1 VERSO - Databases Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8629 2 LIPN - Laboratoire d-Informatique de Paris-Nord

Abstract : We investigate the expressive power of various extensions of first-order, inductive, and infinitary logic with counting quantifiers. We consider in particular a LOGSPACE extension of first-order logic, and a PTIME extension of fixpoint logic with counters. Counting is a fundamental tool of algorithms. It is essential in the case of unordered structures. Our aim is to understand the expressive power gained with a limited counting ability. We consider two problems: i unnested counters, and ii counters with no free variables. We prove a hierarchy result based on the arity of the counters under the first restriction. The proof is based on a game technique that is introduced in the paper. We also establish results on the asymptotic probabilities of sentences with counters under the second restriction. In particular, we show that first-order logic with equality of the cardinalities of relations has a 0-1 law.

Keywords : FINITE MODELTHEORY DESCRIPTIVE COMPLEXITY GENERALIZED QUANTIFIERS INFINITARY LOGIC COUNTING INDUCTIVE LOGIC QUERY LANGUAGES FIRST-ORDER LOGIC





Author: Stéphane Grumbach - Christophe Tollu -

Source: https://hal.archives-ouvertes.fr/



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