I give a semantics for a logic with two pairs of doxastic modals and an indicative conditional connective that all nest without restriction. Sentences are evaluated as accepted, rejected, or neither. Certainty is the necessity-like modality of acceptance. Inferences may proceed from premises that are certain, or merely accepted, or a mix of both. This semantic setup yields some striking results. Notably, the existence of inferences that preserve certainty but not acceptance very directly implies both failure of modus ponens for the indicative conditional in the logic of acceptance and failure of the deduction theorem for the material conditional in the logic of certainty. The latter failure dissolves, in the logic of certainty, the much - discussed tension between modus ponens and the law of import-export.

我给出了一个具有两对 doxastic 模态和一个指示性条件连接词的逻辑的语义，所有这些都没有限制地嵌套。句子被评估为接受、拒绝或两者都不接受。确定性是一种类似于必然的接受方式。推论可以从确定的或仅仅被接受的前提出发，或两者兼而有之。这种语义设置产生了一些惊人的结果。值得注意的是，保留确定性但不接受的推论的存在非常直接地暗示了接受逻辑中指示性条件的前件式失败和确定性逻辑中物质条件的演绎定理的失败。在确定性的逻辑中，后一种失败消除了人们经常讨论的在前处理方式和进出口规律之间的紧张关系。