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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