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.

给定一个条件句 P=>Q（如果 P 则 Q）和相应的事实，观察到人类推理中的四种不同类型的推断：肯定前提（AA）从 P 推出 Q；肯定结论（AC）从 Q 推出 P；否定前提（DA）从 - P 推出 - Q；否定结论（DC）从 - Q 推出 - P。其中，AA 和 DC 在逻辑上是有效的，而 AC 和 DA 在逻辑上是无效的且通常被称为逻辑谬误。然而，人类在日常生活中通常会进行 AC 或 DA 作为实用推理。在本文中，我们在答案集编程中实现了 AC、DA 和 DC 推理。我们引入了八种不同类型的完整性，并通过答案集给出它们的语义。我们研究了形式属性，并对认知心理学中的人类推理任务进行了表征。这些完整性也应用于人工智能中的常识推理。