FROM ORDERING-BASED NONMONOTONIC REASONING TO CONDITIONAL LOGICS

As Gardenfors and Makinson have recently shown, a nonmonotonic inferen ce relation can be generated from a total pre-ordering on the set of f ormulas, or equivalently from an uncertainty valuation. We build here on these results; we include the pre-ordering in the language by intro ducing a conditional operator, and we extend the generation of a nonmo notonic inference relation by allowing the use of incompletely specifi ed pre-orderings. This allows effective procedures for computing nonmo notonic inferences by translating nonmonotonic reasoning into deductio n in a conditional logic.