ON FIRST-ORDER CONDITIONAL LOGICS

Conditional logics have been developed as a basis from which to invest igate logical properties of ''weak'' conditionals representing, for ex ample, counterfactual and default assertions. This work has largely ce ntred on propositional approaches. However, it is clear that for a ful l account a first-order logic is required. Existing or obvious approac hes to first-order conditional logics are inadequate; in particular, v arious representational issues in default reasoning are not addressed by extant approaches. Further, these problems are not unique to condit ional logic, but arise in other nonmonotonic reasoning formalisms. I a rgue that an adequate first-order approach to conditional logic must a dmit domains that vary across possible worlds; as well the most natura l expression of the conditional operator binds variables (although thi s binding may be eliminated by definition). A possible worlds approach based on Kripke structures is developed, and it is shown that this ap proach resolves various problems that arise in a first-order setting, including specificity arising from nested quantifiers in a formula and an analogue of the lottery paradox that arises in reasoning about def ault properties. (C) 1998 Published by Elsevier Science B.V. All right s reserved.