System-Z+: A Formalism for Reasoning with Variable-Strength Defaults

Moisés Goldszmidt, Judea Pearl

We develop a formalism for reasoning with defaults that are expressed with different levels of firmness. Necessary and sufficient conditions for consistency are established, and a unique ranking of the rules is found, called Z+, which renders models as normal as possible subject to the consistency conditions. We provide the necessary machinery for testing consistency, computing the Z+ ranking and drawing the set of plausible conclusions it entails.

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