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

Autonomous agents operating in complex multi-agent environments must reason about what holds from multiple perspectives. Existing approaches often struggle to integrate reasoning across agents and contexts, typically handling these dimensions in separate, specialized modules. This fragmentation can yield brittle and hard-to-maintain reasoning pipelines, particularly when agents must represent and query the beliefs of others (Theory of Mind). We introduce the Observer--Situation Lattice (OSL), a mathematical structure that provides a single, coherent semantic space for perspective-aware cognition. OSL is a finite complete lattice whose elements represent observer--situation pairs, enabling 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 establish formal guarantees for the lattice construction and the correctness and complexity of the proposed algorithms, and we demonstrate practical utility through benchmarks including classic Theory of Mind tasks and comparisons 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.