Cyberlogic: A Foundational Framework for Cross-Space Logic in the Cyber-Physical-Social-Thinking Hyperspace

The convergence of physical, social, and cognitive processes in cyberspace has created the Cyber-Physical-Social-Thinking (CPST) hyperspace, a multidomain environment where entities and interactions span fundamentally distinct logical foundations. Existing space-specific logics, including causal logic in physical space, normative logic in social space, and cognitive logic in thinking space, were not designed for cross-space operation and exhibit critical structural limitations: representational misalignment, nonequivalent mapping, and reasoning inconsistency. Generative AI compounds these challenges by introducing endogenous cyberlogic, which can lead to opaque reasoning and semantic drift in safety-critical contexts. This article presents Cyberlogic, a foundational framework for coordinating logic across the CPST hyperspace. Rather than replacing existing logics, Cyberlogic enables their principled coexistence through a four-layer Entity-Mapping-Reasoning-Governance architecture. It introduces the cyberentity as a unified carrier for cross-space representation, characterizes nonequivalent mappings, and distinguishes between cyberized logic (migrated from other spaces) and endogenous cyberlogic (originating within cyberspace). A formal symbolic system supports rigorous reasoning and extensibility. An information-theoretic perspective, based on mapping entropy and reasoning entropy, complements integrity evaluation by providing a quantitative measure of uncertainty propagation across spaces. Operational principles and the integrity evaluation perspective together guide deployment. The framework is illustrated through a smart city emergency response case study and further substantiated by a prototype implementation with information-theoretic analysis, demonstrating its practical coordination across all layers. Cyberlogic provides a theoretical foundation for organizing cross-space reasoning and governance in the transition from Internet of Things (IoT) to Internet of Everything (IoX), mitigating semantic drift, temporal misalignment, and logical inconsistency as generative AI assumes a greater role in cross-domain decision-making.