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.

中文翻译：

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公理化包含逻辑中的一阶结果

包含逻辑是依赖逻辑的一种变体，它被证明具有与正最大定点逻辑相同的表达能力。包含逻辑不能完全公理化，但它的一阶结果可以公理化。在本文中，我们通过引入包含逻辑的自然演绎系统来提供这样一个明确的部分公理化，该系统对于包含逻辑中的一阶结果是合理和完整的。