A logic for instrumental obligation

TL;DR

This paper introduces a formal logic combining causal reasoning and deontic logic to model instrumental obligations, defining when actions are obligatory based on their causal effectiveness in achieving goals.

Contribution

It develops a novel causal deontic logic with a complete axiomatic system that captures instrumental obligations and permissions, extending prior deontic frameworks.

Findings

The logic is sound and complete.

The decision problem is NP-complete.

It effectively models instrumental obligations and permissions.

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.