Conditional normative reasoning as a fragment of HOL

Abstract

We report on the mechanisation of (preference-based) conditional normative reasoning. Our focus is on Åqvist's system E for conditional obligation, and its extensions. Our mechanisation is achieved via a shallow semantical embedding in Isabelle/HOL. We consider two possible uses of the framework. The first one is as a tool for meta-reasoning about the considered logic. We employ it for the automated verification of deontic correspondences (broadly conceived) and related matters, analogous to what has been previously achieved for the modal logic cube. The equivalence is automatically verified in one direction, leading from the property to the axiom. The second use is as a tool for assessing ethical arguments. We provide a computer encoding of a well-known paradox (or impossibility theorem) in population ethics, Parfit's repugnant conclusion. While some have proposed overcoming the impossibility theorem by abandoning the presupposed transitivity of ‘better than’, our formalisation unveils a less extreme approach, suggesting among other things the option of weakening transitivity suitably rather than discarding it entirely. Whether the presented encoding increases or decreases the attractiveness and persuasiveness of the repugnant conclusion is a question we would like to pass on to philosophy and ethics.