Specifying an Obligation Taxonomy in the Non-Markovian Situation Calculus

Over more than three decades, the Situation Calculus has established itself as an elegant, powerful, and concise formalism for specifying dynamical domains as well as for reasoning about the effects of actions of those domains both in the world and in the mental state of the modelled agents. Moreover, it has also been established that the preconditions of a given action and its effects may be determined entirely by the current situation alone, or they may be determined by past situations as well. When past situations are involved in determining action preconditions and effects, resulting theories are non-Markovian. Assuming a specification of actions that produce obligations, we consider using non-Markovian control in the Situation Calculus to specify different notions of obligations found in the literature. These notions have been specified using Event Calculus; but, as far as we know, they have never been specified using the Situation Calculus. The specifications in this paper yield intuitive properties that ensure the correctness of the whole endeavour.