A logic for instrumental obligation
Jialiang Yan, Qingyu He
TL;DR
This work develops a causal deontic framework to formalize instrumental obligation, defining it as a derived modality via interventions $O_i$ within a priority-based deontic order. By extending structural causal models with P-graphs, it unifies causal reasoning about action outcomes with normative evaluation through a betterness ordering, and introduces instrumental permission $P_i$. The authors prove a sound and complete Hilbert-style calculus $\mathsf{CIO}$ for the resulting logic and show that satisfiability is NP-complete, underscoring the framework’s computational tractability. The approach provides a principled method to determine when an action is the best means to achieve a goal under normative constraints and outlines future work on handling multiple goals and desirability aspects.
Abstract
This paper develops a logic based on causal inferences to formally capture the concept of instrumental obligation. We establish a causal deontic model that extends causal models with priority structures, allowing us to represent both the instrumental and deontic aspects of an obligation. In this framework, instrumental obligation is defined as a derived notion through intervention formulas of causal reasoning, where an action is considered obligatory if it is the best way to achieve the goal. We provide a sound and complete axiomatic system and show that the logic is NP-complete. The concept of instrumental permission is also taken into account in the model.