Abductive reasoning involves finding the missing premise of an “unsaturated” deductive inference, thereby selecting a possible explanans for a conclusion based on a set of previously accepted premises. In this paper, we explore abductive reasoning from a structural proof-theory perspective. We present a hybrid sequent calculus for classical propositional logic that uses sequents and antisequents to define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as explanans when presented with an abductive problem. Specifically, we show that this set may not include the deductively minimal hypothesis due to the presence of redundant information. We also establish that the set of all analytic hypotheses exhausts all possible solutions to the given problem. Finally, we propose a deductive criterion for differentiating between the best explanans candidates and other hypotheses.

溯因推理涉及找到“不饱和”演绎推理中缺失的前提，从而根据一组先前接受的前提为结论选择可能的解释。在本文中，我们从结构证明理论的角度探讨溯因推理。我们提出了一种经典命题逻辑的混合序列演算，它使用后继和反后继来定义一个过程，用于识别一组分析假设，理性主体将选择这些假设作为解释当遇到溯因问题时。具体来说，我们表明，由于存在冗余信息，该集合可能不包括演绎最小假设。我们还确定所有分析假设的集合穷尽了给定问题的所有可能的解决方案。最后，我们提出了区分最佳解释候选者和其他假设的演绎标准。