This paper proposes a Situation Calculus solution to the frame problem for obligation-producing actions, which are actions that create obligations on the part of the agent that performs them. As an example of such actions, we have an opening door action performed by an agent, which has the subsequent obligation of getting the door closed. Demolombe and others extend Raymond Reiter's solution to the frame problem for ordinary actions to accommodate obligation-producing actions. Obligation-producing actions do affect the truth value of a newly introduced fluent that captures the accessibility relation used in semantics of obligation modalities in the Situation Calculus. Our work simplifies Demolombe's characterization of the accessibility relation by eliminating the notion of ideality of situations, thereby remaining close to Kripke-style possible-world semantics for deontic logic, in the spirit of Governatori's approach. Furthermore, we spell out details of a complete solution by extending basic action theories of Reiter to the new setting. Finally, we extend Reiter's regression operator for reasoning about actions back to the initial situation to this new setting. Our solution yields intuitive properties that one would expect from obligations: for example, if a sentence is obligatory to an agent in a given situation, it remains so in subsequent situations unless the obligation is explicitly stopped.

翻译：本文提出一种情景演算框架，用以解决产生义务的动作的框架问题——这类动作会使执行它的主体承担相应义务。例如，主体执行开门的动作后，便负有随后关门之义务。Demolombe等人将Raymond Reiter针对普通动作的框架问题解决方案扩展到了产生义务的动作。产生义务的动作会影响一个新引入流谓词的真值，该流谓词捕捉了情景演算中义务模态语义所使用的可达关系。本研究通过消除情景理想性的概念，简化了Demolombe对可达关系的刻画，从而在Governatori方法的框架下，更接近道义逻辑的Kripke式可能世界语义。此外，我们将Reiter的基本动作理论扩展到新设定中，详细阐明了一个完整解决方案的具体细节。最后，我们将Reiter用于回溯初始情景进行动作推理的回归算子扩展到这一新设定中。我们的解决方案产生了符合义务直觉的优良性质：例如，若某语句在给定情景中对主体具有义务性，则除非该义务被显式终止，在后续情景中该义务仍将持续成立。