Towards an Intuitionistic Deontic Logic Tolerating Conflicting Obligations

We propose a minimal deontic logic, called MIND, based on intuitionistic logic. This logic gives a very simple solution to handling conflicting obligations: the presence of two conflicting obligations does not entail the triviality of the set of norms. Moreover, the logic supports the claim that there may be no obligations at all, so that a logical truth is not obligatory. Like in intuitionistic/constructive modal logic, in this logic, the two deontic modalities Obligation and Permission are not dual, however as a difference with so-called constructive modal logic, it supports distribution of permission over disjunction, but it does not satisfy aggregation of obligations. The logic MIND is a non-normal modal logic based on intuitionistic logic and it is semantically characterised by a suitable neighbourhood semantics. We further present a simple cut-free sequent calculus for this logic. By means of this calculus we show that logic MIND is decidable and that it satisfies the disjunction property.