From ordering-based nonmonotonic reasoning to conditional logics

Abstract

As Gärdenfors and Makinson have recently shown, a nonmonotonic inference relation can be generated from a total pre-ordering on the set of formulas, or equivalently from an uncertainty valuation. We build here on these results; we include the pre-ordering in the language by introducing a conditional operator, and we extend the generation of a nonmonotonic inference relation by allowing the use of incompletely specified pre-orderings. This allows effective procedures for computing nonmonotonic inferences by translating nonmonotonic reasoning into deduction in a conditional logic.