Deontic logic aims at formally modeling the reasoning with norm-related modalities. Von Wright recognized that the obligation modality bears a resemblance to modal necessity and the permission modality to modal possibility, which resulted in his Standard Deontic Logic [9]. SDL is the modal logic KD. Since its conception, SDL has drawn a lot of criticism: e.g., Chisholm [2] argued that it was unfit to represent certain types of conditional obligation, and Makinson [5] and van der Torre [6] emphasized that deontic logic is much more naturally studied as a process of iterative detachment relative to explicitly represented normative systems; a view that does not fit well with the modal logic modeling proposed by Von Wright. One way in which SDL, but also most other systems of deontic logic, falls short is the treatment of action with uncertain, probabilistic or attempted effects. Yet it is very natural, and sometimes even crucial for rational decision making, to reason, for instance, about being forbidden to take certain risks, being obliged to try something, or to avoid being liable for an attempted crime (see [10] for an excellent philosophical discussion of the role of attempt in criminal law). In our view, the modalities involved in these cases can all be viewed as applying to probabilistic action, that is, action with a certain chance of success. In particular, we suggest to model attempts as actions maximizing subjective probabilities of action success [1]. This modeling of attempt is quite different from other approaches in the literature. Placek [7] aims to define attempt entirely in terms of objective, non-mental modalities. Vanderveken [8] does take a subjective stance, but does not use probabilities or any other means to represent subjective epistemic attitudes. Finally, Herzig and Lorini [4] see attempt as an internal mental action preceding the objective external action. The first question we will discuss is how the obligation to attempt an action can be suitably modeled in a probabilistic stit framework extended with deontic modalities.
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