  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.
