Don't ever do that! Long-term duties in PDeL

Abstract

This paper studies long-term norms concerning actions. In Meyer's Prepositional Deontic Logic (PDeL), 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 PDeL 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 / (indebtedness) to represent the condition that an agent has some unfulfilled obligation. © Springer-Verlag Berlin Heidelberg 2006.