On first-order conditional logics

摘要

Conditional logics have been developed as a basis from which to investigate logical properties of “weak” conditionals representing, for example, counterfactual and default assertions. This work has largely centred on propositional approaches. However, it is clear that for a full account a first-order logic is required. Existing or obvious approaches to first-order conditional logics are inadequate; in particular, various representational issues in default reasoning are not addressed by extant approaches. Further, these problems are not unique to conditional logic, but arise in other nonmonotonic reasoning formalisms. I argue that an adequate first-order approach to conditional logic must admit domains that vary across possible worlds; as well the most natural expression of the conditional operator binds variables (although this binding may be eliminated by definition). A possible worlds approach based on Kripke structures is developed, and it is shown that this approach 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 default properties.