Constructive Circumscription

Circumscription is one of the most powerful nonmonotonic reasoning formalisms. Its classical modeltheoretic semantics serves as an effective mechanism to ensure minimality in commonsense reasoning. However, as the lack of proof-theoretic feature, it is incapable of expressing derivation order that sometimes plays a crucial role in various reasoning tasks. On the other hand, the general theory of stable models has a similar logic formulation to circumscription but takes supportedness into account, although it does not satisfy the minimality criterion in general. In this paper, we introduce the notion of constructive circumscription. Unlike the original circumscription, constructive circumscription enforces both minimality and derivation order. Such derivation order is achieved by strengthening the underlying circumscriptive theory with a first-order formula called explicit construction formula. With constructive circumscription, minimal models are only considered under an explicit constructibility. We study properties of constructive circumscription in details, and compare it with circumscription, the general theory of stable models, and the FLP semantics.