A Simple Doxastic Deontic Logic for Norm-Guided Decision Making

Abstract:Making decisions despite conflicting norms and incomplete or unreliable information is a fundamental challenge for autonomous systems. We introduce a simple doxastic deontic logic for this setting: a classically reducible fragment of Chellas' Minimal Deontic Logic, extended with explicit conditional norms and combined with multi-agent KD45, so that norms can depend on agents' beliefs about both facts and norms. On this logic we define the Doxastic Norm Compliance Optimization Problem, where an agent chooses a decision minimizing weighted norm violations. We distinguish subjective optimization (relative to the agent's beliefs) from objective optimization (relative to the actual facts). We give conditions under which (i) the two coincide and (ii) optimal decision-making can be reduced to weighted partial MaxSAT in polynomial time.

Manuscript accepted at PRIMA 2026. Includes an additional appendix with proofs

Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)

arXiv:2610.00668 [cs.AI]

(or arXiv:2610.00668v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.00668 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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