Classification and deontic explosion for contrary-to-duty obligations

TL;DR

This paper analyzes a recent deontic logic system, demonstrating a limited deontic explosion phenomenon and providing a novel classification of models based on a single forbidden world.

Contribution

It reveals a limited deontic explosion in Carmo and Jones' latest system and offers a surprising model classification approach.

Findings

Limited deontic explosion: any non-highest grade is acceptable if the highest is not achieved.

All models satisfying the strongest 1997 system can be characterized by one forbidden world.

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.