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An abstract, argumentation-theoretic approach to default reasoning

Andrei Bondarenko, Phan Minh Dung, Robert Kowalski, Francesca Toni

Journal Article
Artificial Intelligence
Volume 93
Issues 1–2
Elsevier Science Bv

We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions.

An assumption can be defeated (or "attacked") if its "contrary" can be

proved, possibly with the aid of other conflicting assumptions. We show

that, given such a framework, the standard semantics of most logics for

default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set.

We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic programming. We regard a set of assumptions, in general, as admissible if and only if it is conflict-free and defends itself (by attacking) every set of assumptions which attacks it. We identify conditions for the existence of extensions

and for the equivalence of different semantics.

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