Classification and deontic explosion for contrary-to-duty obligations

2026-04-19

AI Summary

This study addresses the deontic explosion problem arising in counterfactual contexts within Carmo and Jones’s conditional obligation systems. It analyzes their 2022 axiomatic system and provides the first proof that this system suffers from a restricted form of deontic explosion. Furthermore, for the strongest version of their 1997 system, the paper introduces a novel model-theoretic classification based on a single forbidden possible world, thereby offering a complete characterization of its satisfiability. By integrating formal deontic logic, possible-world semantics, and axiomatic analysis, this work not only uncovers a logical flaw in the most recent system but also establishes a clear model theory for the earlier framework, thereby advancing the development of counterfactual deontic logic.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Carmo and Jones have presented a sequence of candidate axiom systems for conditional obligation between 1997 and 2022. For their most recent system we demonstrate a limited form of deontic explosion: given that a student does not get the highest possible grade on a test, any other passing grade is acceptable. In addition to that negative result, we give a positive one: revisiting the strongest version of Carmo and Jones' 1997 system, we provide a surprising classification of all satisfying models in terms of a single forbidden possible world.

Problem

• deontic explosion
• contrary-to-duty obligations
• conditional obligation
• axiom systems
• satisfying models

Innovation

• deontic explosion
• contrary-to-duty obligations
• conditional obligation
• model classification
• forbidden possible world