*Damir Dzhafarov, Stefan Kaufmann, Bjørn Kjos-Hanssen, Dave Ripley, et al., at the 2016 ASL Annual Meeting at UConn.*

Slides

José Carmo and Andrew J.I. Jones have studied contrary-to-duties obligations in a series of papers.

They develop a logical framework for scenarios such as the following:

1. There ought to be no dog.

2. If there is a dog, there ought to be a fence.

One conjecture from Carmo and Jones 1997 was refuted in a rather technical way in my 1996 term paper at University of Oslo.

The conjecture stated that one could simply add the condition

$\DeclareMathOperator{\pii}{ob}$

$$

(Z \in \pii(X)) \land

(Y \subseteq X) \land

(Y \cap Z \ne \emptyset ) \rightarrow (Z \in \pii(Y )) \tag{5e}

$$

for the conditional obligation operator ob.

In a follow-up paper (2001) they argued that (5e) could be added by weakening some other conditions.

In a new paper in Studia Logica, and presented at the Association for Symbolic Logic Annual Meeting 2016 at UConn, I argue that (5d) and (5e) are in conflict with each other. The argument is a generalization and strengthening of the 1996 argument.

2018: Benzmüller et al. have implemented Carmo and Jones’ logic in the proof assistant Isabelle.

## Professor of Mathematics, University of Hawaii at Manoa