Abstract
We study the extension of dependence logic \(\mathcal {D}\) by a majority quantifier \(\mathsf{M}\) over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all arities. Our results imply that, from the point of view of descriptive complexity theory, \(\mathcal {D}(\mathsf{M})\) captures the complexity class counting hierarchy. We also obtain characterizations of the individual levels of the counting hierarchy by fragments of \(\mathcal {D}(\mathsf{M})\).
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We thank the anonymous referees for helpful remarks.
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The third author was supported by Grants 264917 and 275241 of the Academy of Finland. The second and fourth author were supported by a Grant from DAAD within the PPP programme. The fourth author was also supported by DFG Grant VO 630/6-2.
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Durand, A., Ebbing, J., Kontinen, J. et al. Dependence Logic with a Majority Quantifier. J of Log Lang and Inf 24, 289–305 (2015). https://doi.org/10.1007/s10849-015-9218-3
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DOI: https://doi.org/10.1007/s10849-015-9218-3