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Axiomatizing first-order consequences in inclusion logic (1904.06227v2)
Published 12 Apr 2019 in math.LO and cs.LO
Abstract: Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In this paper, we provide such an explicit partial axiomatization by introducing a system of natural deduction for inclusion logic that is sound and complete for first-order consequences in inclusion logic.