Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.

翻译：给定条件语句“P=>Q”（如果P则Q）及相关事实，人类推理中观察到的推理类型有四种：肯定前件（AA）（或假言推理）由P推出Q；肯定后件（AC）由Q推出P；否定前件（DA）由¬P推出¬Q；否定后件（DC）（或拒取式）由¬Q推出¬P。其中，AA和DC在逻辑上是有效的，而AC和DA在逻辑上无效，常被称为逻辑谬误。然而，人类在日常生活中的实用推理却经常使用AC或DA。本文在回答集编程中实现了AC、DA和DC推理，引入了八种不同类型的补全形式，并通过回答集给出其语义。我们研究了相关形式化属性，并刻画了认知心理学中的人类推理任务。这些补全形式也被应用于人工智能的常识推理。