The Chisholm Paradox and the Situation Calculus

Deontic logic is appropriate to model a wide variety of legal arguments, however this logic suffers form certain paradoxes of which the so-called Chisholm is one of the most notorious. We propose a formalisation of the Chisholm set in the framework of the situation calculus. We utilise this alternative to modal logic for formalising the obligations of the agent and avoiding the Chisholm paradox. This new approach makes use of the notion of obligation fluents together with their associated successor state axioms. Furthermore, some results about automated reasoning in the situation calculus can be applied in order to consider a tractable implementation.