  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 paradox.
