A Logic of Objective and Subjective Oughts (full paper with proofs)

TL;DR

This paper introduces a formal logic integrating objective and subjective oughts, extending the stit framework with deontic and epistemic operators to better model responsibility and ethical considerations in AI.

Contribution

It presents a new axiomatization and semantics for a logic of objective and subjective oughts, addressing key puzzles in knowledge and obligation.

Findings

Provides soundness and completeness proofs for the logic.

Addresses Horty's puzzles for knowledge and obligation.

Extends the stit paradigm with deontic and epistemic operators.

Abstract

The relation between agentive action, knowledge, and obligation is central to the understanding of responsibility --a main topic in Artificial Intelligence. Based on the view that an appropriate formalization of said relation would contribute to the development of ethical AI, we point out the main characteristics of a logic for objective and subjective oughts that was recently introduced in the literature. This logic extends the traditional stit paradigm with deontic and epistemic operators, and provides a semantics that deals with Horty's puzzles for knowledge and obligation. We provide an axiomatization for this logic, and address its soundness and completeness with respect to a class of relevant models.