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Journal of Logic and Computation, Volume 7, Issue 6: December 1997.
A first-order conditional logic with qualitative statistical semantics
Computer Science Department, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada. E-mail: firstname.lastname@example.org
We define a first-order conditional logic in which conditionals, such as [agr] [rarr] [bgr], are interpreted as saying that normal/common/typical objects which satisfy [agr] satisfy [bgr] as well. This qualitative 'statistical' interpretation is achieved by imposing additional structure on the domain of a single first-order model in the form of an ordering over domain elements and tuples. [agr] [rarr] [bgr] then holds if all objects with property [agr] whose ranking is minimal satisfy [bgr] as well. These minimally ranked objects represent the typical or common objects having the property [agr]. This semantics differs from that of the more common subjective interpretation of conditionals, in which conditionals are interpreted over sets of standard first-order structures. Our semantics provides a more natural way of modelling qualitative statistical statements, such as 'typical birds fly', or 'normal birds fly'. We provide a sound and complete axiomatization of this logic, and we show that it can be given probabilistic semantics.
Key words: Conditional logic, first-order logic, qualitative statistical reasoning, nonmonotonic logic