In this paper, we present a first-order and a propositional logic for reasoning about degrees of confirmation. We define the appropriate formal languages and describe the corresponding classes of models. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. We also show that our propositional logic is decidable. For some restrictions of the logics, we provide finitary axiomatic systems.

中文翻译：

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推理确认度的逻辑

在本文中，我们提出了用于推理确认度的一阶和命题逻辑。我们定义了适当的形式语言并描述了相应的模型类。我们为这两种逻辑提供了无限的公理化，并且我们证明了这些公理化是合理的并且非常完整的。我们还证明了我们的命题逻辑是可判定的。对于逻辑的一些限制，我们提供有限的公理系统。