A Semantics for "Typically" in First-Order Default Reasoning

We present a new semantics for first-order conditional logic, which is a generalization of that of Friedman, Halpern and Koller [7]. We utilize Fitting's embedding of first-order classical logic in first-order S4 to define our semantics. We explain our semantics by showing how it works on the connective expressing "typically implies". We argue that it has a number of good properties, in particular, it is more adjustable to special situations than that of [7]. For example, we can make sense of nested conditional implications even when a conditional implication does not necessarily hold on the entire set of possible worlds, but where-ever it is satisfied, the conclusion is typically satisfied.