Designing a Deontic Logic of Deadlines

This paper studies the logic of a dyadic modal operator for being obliged to meet a condition ρ before a condition δ becomes true. Starting from basic intuitions we arrive at a simple semantics for deadline obligations in terms of branching time models. We show that this notion of deadline obligation can be characterized in the branching time logic CTL. The defined operator obeys intuitive logic properties, like monotony w.r.t. ρ and anti-monotony w.r.t. δ, and avoids some counterintuitive properties like agglomeration w.r.t ρ and ‘weak agglomeration’ w.r.t. δ. However, obligations of this type are implied by the actual achievement of ρ before the deadline. We argue that this problem is caused by the fact that we model the obligation only from the point of view of its violation conditions. We show that the property might be eliminated by considering success conditions also.