arXiv:2609.07483cs.AI2026-09

提出三种基于不同否定逻辑的反事实推理模型,统一了形式结构。

Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation

  • 区分矛盾、对立、中介三类否定,构建对应模态推理规则
  • 证明三类反事实推理结论真值等于前提中否定部分真值
  • 为非经典逻辑中的反事实推理提供统一算法框架,适合逻辑研究者

模态否定(MT)是经典逻辑推理规则,反事实是与事实相反的假设性陈述,反事实推理基于反事实展开。否定是三者的核心概念。本文基于包含矛盾否定、对立否定和中介否定的逻辑系统LCOI&PLCOI,提出三种对应的模态否定变体:基于矛盾否定的MTC、基于对立否定的MTO、基于中介否定的MTI。定义了三者中的蕴含关系,给出其真值计算算法,并讨论算法可约性。为将三类否定融入反事实及其推理,根据是否具备逻辑否定,将反事实分为两类,进而提出三种基于不同逻辑否定的反事实及其推理。本文进一步论证,这三类反事实推理的推导形式分别与MTC、MTO、MTI一致。因此,MTC、MTO、MTI的真值算法可直接用于三类反事实推理。算法表明:若推理第一前提为真,则结论真值等于各前提中否定部分的真值。这体现了算法的一致性与准确性。

原文摘要 · Abstract (English)

Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfactual reasoning is a process of reasoning based on counterfactuals. Negation is an indispensable core concept in them. In this paper, based on the logical systems LCOI&PLCOI with contradictory negation, opposite negation and intermediary negation, we propose three variants of Modus Tollens corresponding to distinct negation types, namely MTC: Modus Tollens based on contradictory negation, MTO: Modus Tollens based on opposite negation, and MTI: Modus Tollens based on intermediary negation. We define the implications within MTC, MTO and MTI, provide the truth value algorithms of MTC, MTO and MTI, and discuss the reducibility of these algorithms. To incorporate these three types of negation into counterfactuals and counterfactual reasoning, we differentiate counterfactuals into two types based on whether they possess logical negation, thereby proposing three counterfactuals and counterfactuals reasoning based on different logical negations. In this paper, we further argue that the three counterfactuals reasoning based on different logical negations have the same inference form as MTC, MTO and MTI, respectively. In other words, they share the same inference structure. As a result, the truth value algorithms for MTC, MTO and MTI can be as the truth value algorithms for the three counterfactuals reasoning based on different logical negations. The algorithms indicates that if the first premise of the reasoning is true, the truth values of the reasoning conclusions are identical to the truth values of the three negative premises in the reasoning premises, respectively. This reflects the consistency and accuracy of the truth value algorithms.

逻辑推理反事实否定

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