Conditional First-Order Logic Revisited
N. Friedman, J. Y. Halpern, and D. Koller
National Conf. on Artificial Intelligence (AAAI96).
Conditional logics play an important role in recent
attempts to investigate default reasoning.
We show that a straightforward definition of first-order
conditional logic using preferential structures, such
as Delgrande's conditional logic, encounters several problems.
cannot handle exceptional individuals, a problem that is
an infinitary version of the lottery paradox.
We take a different approach, using the notion of plausibility
spaces. This is a notion that generalizes a number of
different semantics for defaults, including preferential
As we show here in a
first-order setting, plausibility spaces provide the necessary
expressive power we need to deal with the lottery
paradox and its variants. We claim that our approach provides the most
natural extension of the KLM properties to a first-order language.
we provide a sound and complete axiomatization of our logic that
contains only the KLM properties and standard axioms of
first-order modal logic.
Plausibility spaces give us the tools to analyze the obvious
first-order extensions of
and the approaches of of Delgrande and of Lehmann &
Magidor, and to understand the difficulties they encounter.
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