A Dynamic Deontic Simplicial Logic for Joint Commitments
This work offers a novel logical framework for representing and reasoning about group obligations and joint actions, addressing a gap in deontic logic for multi-agent systems.
The paper introduces Deontic Simplicial Logic (DSL) and its dynamic extension DDSL, providing the first deontic interpretation of simplicial complexes to model group obligations and joint commitments. Soundness and completeness are proven for both logics.
In this paper we introduce the novel Deontic Simplicial Logic (DSL), a deontic logic for group obligations based on simplicial complexes. We provide the first deontic interpretation of simplicial models in which vertices represent individual commitments and higher-dimensional simplices represent joint obligations of groups of agents. We further extend DSL to the Dynamic Deontic Simplicial Logic (DDSL), resulting in the first dynamic logic based on simplicial complexes. DDSL models agents' choices among mutually exclusive commitments and captures the effects of individual and joint actions via update operations on simplicial models. We prove soundness and completeness for both the static and dynamic deontic simplicial logics. We motivate our results with multiple examples, both in the static and dynamic settings.