The Observer-Situation Lattice: A Unified Formal Basis for Perspective-Aware Cognition

Abstract: Autonomous agents operating in complex, multi-agent environments must reason about what is true from multiple perspectives. Existing approaches often struggle to integrate the reasoning of different agents, at different times, and in different contexts, typically handling these dimensions in separate, specialized modules. This fragmentation leads to a brittle and incomplete reasoning process, particularly when agents must understand the beliefs of others (Theory of Mind). We introduce the Observer-Situation Lattice (OSL), a unified mathematical structure that provides a single, coherent semantic space for perspective-aware cognition. OSL is a finite complete lattice where each element represents a unique observer-situation pair, allowing for a principled and scalable approach to belief management. We present two key algorithms that operate on this lattice: (i) Relativized Belief Propagation, an incremental update algorithm that efficiently propagates new information, and (ii) Minimal Contradiction Decomposition, a graph-based procedure that identifies and isolates contradiction components. We prove the theoretical soundness of our framework and demonstrate its practical utility through a series of benchmarks, including classic Theory of Mind tasks and a comparison with established paradigms such as assumption-based truth maintenance systems. Our results show that OSL provides a computationally efficient and expressive foundation for building robust, perspective-aware autonomous agents.