The Varieties of Ought-Implies-Can and Deontic STIT Logic

2026-04-01

AI Summary

This study addresses the philosophical diversity surrounding the “Ought-implies-Can” (OiC) principle in multi-agent systems by proposing a modular deontic STIT logic framework. The work systematically integrates and formally reconstructs ten distinct interpretations of OiC, combining STIT logic, deontic logic, and sequent calculus techniques to develop multiple sound and complete formal systems. Beyond enabling precise characterizations of each variant of the principle, the framework introduces commitment axioms that uncover the logical entailments and hierarchical relationships among these interpretations. This contribution establishes a unified logical foundation for normative reasoning in multi-agent contexts, accommodating the nuanced philosophical commitments underlying different readings of Ought-implies-Can.

Technology Category

Multiagent Systems: Agreement, Argumentation & NegotiationReasoning under Uncertainty: Other Foundations of Reasoning under UncertaintyKnowledge Representation and Reasoning: Argumentation

Application Category

Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactionsEconomics, Online Markets and Human Computation: Fairness and ethical considerations in crowd work and in human-in-the-loop AI systemsResponsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings.

Problem

• Ought-implies-Can
• Deontic STIT Logic
• multi-agent choice-making
• logical relations
• philosophical interpretations

Innovation

• deontic STIT logic
• Ought-implies-Can
• sequent calculus
• modal logic
• multi-agent choice