A Simple Doxastic Deontic Logic for Norm

The research introduces a simple doxastic deontic logic designed for decision-making under conflicting norms and incomplete information, which is a challenge for autonomous systems. This logic is a fragment of Chellas' Minimal Deontic Logic, extended to include explicit conditional norms and integrated with multi-agent KD45 to allow norms to depend on agents' beliefs about both facts and other norms. The framework defines a Doxastic Norm Compliance Optimization Problem where an agent selects a decision that minimizes weighted norm violations. The work distinguishes between subjective optimization, relative to the agent’s beliefs, and objective optimization, relative to actual facts. The research establishes conditions under which these two forms of optimization coincide and demonstrates that optimal decision-making can be reduced to weighted partial MaxSAT in polynomial time.

The work addresses the fundamental difficulty autonomous systems face when navigating normative conflicts and uncertainty, moving beyond standard logic into a framework that explicitly models the relationship between belief, norms, and optimal action. The move from classical deontic logic to a doxastic extension suggests a necessary shift in how AI handles context; instead of assuming static truth, agents must reason about their own epistemic states (beliefs) when adhering to obligations. The connection to MaxSAT implies that this complex normative reasoning can be translated into a computationally tractable optimization problem. A key implication is whether the polynomial-time reduction truly captures the necessary complexity required for robust moral reasoning, or if it represents an accessible, but potentially simplified, formalization of real-world norm compliance. Future work must scrutinize the boundaries between subjective and objective optimization to see if the coincidence conditions map onto meaningful constraints in complex multi-agent scenarios, and whether this simplification compromises the fidelity of normative judgment.