Weighted Defaults in Description Logics: Formal Properties and Proof Theory

We present a Preferential Default Description Logic (pddl) based on weighted defaults and show that the preferential entailment relation ∑ satisfies all properties of system P and Rational Monotonicity. The main characteristics of this pddl is that it uses an ordering between multisets of defaults for priorization, treats defaults similar to material implications, and adheres strictly to the principle of exception minimization.

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