'What I Fail to Do Today, I Have to Do Tomorrow': A Logical Study of the Propagation of Obligations

We study a logical property that concerns the preservation of future directed obligations that have not been fulfilled yet. We call this property 'propagation property'. The goal is to define a combination of temporal and deontic logics which satisfies this property. Our starting point is the product of temporal and deontic logics. We investigate some modifications of the semantics of the product in order to satisfy the propagation property, without losing too much of the basic properties of the product. We arrive at a semantics in which we only consider ideal histories that share the same past as the current one, and that enables an interesting characterization of the states in which obligations propagate: these are the states where there are no violations of present directed obligations.