Obligation-Producing Actions

2026-06-12

AI Summary

This work addresses the formalization challenge of obligation-generating actions in the situation calculus by proposing a novel framework that dispenses with the notion of ideal situations. It introduces a Kripke-semantics-based accessibility relation to model deontic modalities and extends Reiter’s basic action theory along with the regression operator, thereby enabling a natural representation of the generation, persistence, and termination of obligations. By abandoning Demolombe et al.’s assumption of ideal situations, the approach simplifies the semantic structure while preserving formal rigor, thus supporting effective reasoning about obligations in dynamic environments.

Abstract

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.

Problem

• obligation-producing actions
• frame problem
• Situation Calculus
• deontic logic
• accessibility relation

Innovation

• obligation-producing actions
• Situation Calculus
• frame problem
• deontic logic
• regression operator