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：给定一个条件语句P=>Q（如果P则Q）及其相关事实，人类推理中可观察到四种不同类型的推断：肯定前件（AA，即取模 ponens）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，即取模 tollens）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，人类在日常生活中常将AC或DA作为语用推断使用。本文在回答集编程中实现了AC、DA和DC推断，引入了八种不同类型的完备化，并通过回答集给出其语义。我们研究了形式化性质，并对认知心理学中的人类推理任务进行了刻画。这些完备化方法也被应用于人工智能中的常识推理。