否定后件式与反事实及基于三种否定类型的反事实推理
Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation
- Institute of Mathematics and Physics, Jiangnan University（江南大学数学与物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文基于三种否定类型提出否定后件式变体MTC、MTO和MTI，将其融入反事实推理，证明二者共享推理结构，并给出真值算法，体现一致性与准确性。
AI中文摘要：
否定后件式（Modus Tollens, MT）是一种经典的逻辑推理规则，而反事实是违背事实的假设性陈述，反事实推理则是基于反事实的推理过程。否定是它们中不可或缺的核心概念。本文基于具有矛盾否定、对立否定和中介否定的逻辑系统LCOI&PLCOI，提出了对应于不同否定类型的三种否定后件式变体，即MTC：基于矛盾否定的否定后件式，MTO：基于对立否定的否定后件式，以及MTI：基于中介否定的否定后件式。我们定义了MTC、MTO和MTI中的蕴涵，给出了MTC、MTO和MTI的真值算法，并讨论了这些算法的可归约性。为了将这三种否定类型融入反事实和反事实推理，我们根据反事实是否具有逻辑否定将其区分为两种类型，从而提出了基于不同逻辑否定的三种反事实及反事实推理。在本文中，我们进一步论证，基于不同逻辑否定的三种反事实推理分别与MTC、MTO和MTI具有相同的推理形式。换言之，它们共享相同的推理结构。因此，MTC、MTO和MTI的真值算法可以作为基于不同逻辑否定的三种反事实推理的真值算法。这些算法表明，如果推理的第一个前提为真，则推理结论的真值与推理前提中三个否定前提的真值分别相同。这反映了真值算法的一致性和准确性。
英文摘要：
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.
