A Ranking Semantics for First-Order Conditionals

Usually, default rules in the form of conditional statements are built on propositional logic, representing classes of individuals by propositional variables, as in “Birds fly, but penguins don't”. Only few approaches have addressed the problem of giving formal semantics to first-order conditionals that allow (nonmonotonic) inferences both for classes and for individuals. In this paper, we present a semantics for first-order conditionals that is based on ordinal conditional (or ranking) functions which are well-known in the area of propositional default reasoning and makes use of representative individuals to establish conditional relationships. We generalize the c-representation approach of [8] for inductive reasoning with first-order conditionals, and evaluate our approach via benchmark examples and a catalogue of general properties.