Common-sense reasoning in constructive discursive logic

We consider common-sense reasoning in constructive discursive logic, which is a constructive version of Jaskowski´s discursive logic. We discuss two problems in common-sense reasoning, i.e., paraconsistent and non-monotonic reasoning. First, we show that the logic can formalize paraconsistent reasoning, which can be inconsistent but nontrivial. Second, we argue that the logic can be used to express non-monotonic reasoning, in which old conclusions can be invalidated by new information. We also suggest future problems related to the proposed logic.