Conditional First-Order Logic Revisited
N. Friedman, J. Y. Halpern, and D. Koller
Submitted for publication, 1999.
Conditional logics play an important role in recent attempts to
formulate theories of default reasoning. This paper investigates first-order
conditional logic. We show that, as for first-order probabilistic
logic, it is important not to confound statistical conditionals
over the domain (such as "most birds fly''), and subjective conditionals
over possible worlds (such as "I believe that Tweety is unlikely to fly").
We then address the issue of ascribing semantics to first-order conditional
logic. As in the propositional case, there are many possible semantics.
To study the problem in a coherent way, we use plausibility structures.
These provide us with a general framework in which many of the standard
approaches can be embedded. We show that while these standard approaches
are all the same at the propositional level, they are significantly different
in the context of a first-order language. Furthermore, we show that plausibilities
provide the most natural extension of conditional logic to the first-order
case: We provide a sound and complete axiomatization that contains only
the KLM properties and standard axioms of first-order modal logic.
We show that most of the other approaches have additional properties, which
result in an inappropriate treatment of an infinitary version of the lottery
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