Abstract
In this paper, we are going to present a new notion of “extension” for defeasible inheritance networks that allows us to deal with cyclic nets. Horty has shown that cyclic nets need not have extensions in the sense of Touretzky. This paper presents a generalization of that notion of extension that can be applied to cyclic nets. The present proposal is inspired by a somewhat unexpected analogy between cyclic nets and “semantically closed” languages, i.e., languages containing their own truth predicate. Accordingly, this approach to defeasible inheritance networks with cycles shows similarities to the solution of semantic paradoxes put forth by Kripke.
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