Counterfactual Conditionals in Quantified Modal Logic

Abstract: We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more generally, theory-of-mind reasoning systems) should be at least as expressive as first-order (quantified) modal logic (QML) to be well-behaved. While existing work on moral reasoning has focused on counterfactual-free QML moral reasoning, we present a fully specified and implemented formal system that includes counterfactual conditionals. We validate our model with two projects. In the first project, we demonstrate that our system can be used to model a complex moral principle, the doctrine of double effect. In the second project, we use the system to build a data-set with true and false counterfactuals as licensed by our theory, which we believe can be useful for other researchers. This project also shows that our model can be computationally feasible.