Don't ever do that! : long-term duties in PDel

This paper studies long-term norms concerning actions. In Meyer’s Propositional Deontic Logic (PD e L), only immediate duties can be expressed, however, often one has duties of longer durations such as: "Never do that", or "Do this someday". In this paper, we will investigate how to amend PD e L so that such long-term duties can be expressed. This leads to the interesting and suprising consequence that the long-term prohibition and obligation are not interdefinable in our semantics, while there is a duality between these two notions. As a consequence, we have provided a new analysis of the long-term obligation by introducing a new atomic proposition I (indebtedness) to represent the condition that an agent has some unfulfilled obligation.