A Simple Doxastic Deontic Logic for Norm-Guided Decision Making

2026-09-30

AI Summary

This study addresses the decision-making challenges faced by autonomous systems under normative conflicts and incomplete information. It pioneers the integration of multi-agent KD45 belief logic with Chellas’s minimal deontic logic to construct a reasoning framework supporting belief-based conditional norms. By formulating a compliance optimization problem that distinguishes between subjective and objective perspectives, this work proposes a weighted partial MaxSAT solving algorithm. The research demonstrates that subjective and objective optimizations are equivalent under specific conditions, and reduces optimal decision-making to MaxSAT solving in polynomial time. Consequently, this approach provides an efficient and reliable decision-making methodology for autonomous systems operating in complex environments.

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.

Problem

• autonomous systems
• conflicting norms
• incomplete information
• norm-guided decision making
• deontic logic

Innovation

• Doxastic Deontic Logic
• Norm-Guided Decision Making
• Weighted Partial MaxSAT
• Multi-Agent KD45
• Norm Compliance Optimization