This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of conditional reasoning: (i) a logic C of inference from certain premises; and (ii) a logic U of inference from uncertain premises. But whereas C is monotonic for the conditional, U is not, and whereas C obeys Modus Ponens, U does not without restrictions. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use the distinction between the two systems to cast light, in particular, on McGee's puzzle about Modus Ponens. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences.

翻译：本文为自然语言中指示性条件句的真值条件与概率建立了一种三值语义学。该框架基于W. Cooper首次提出的三值真值条件，并衍生出两类条件推理逻辑：（i）确定性前提推理逻辑C；及（ii）不确定性前提推理逻辑U。然而，C对条件句具有单调性，而U则不具备；且C遵循肯定前件规则，但U在无限制条件下则不遵循。我们系统论证了这两种框架下推理的三值表征与概率表征之间的对应关系，并借助两个系统的区分，特别阐释了麦吉关于肯定前件规则的悖论。最终形成了对指示性条件句语义学与认识论问题的统一解释，可有效应用于分析条件推理的有效性。