{"ID":2894823,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.00853","arxiv_id":"2508.00853","title":"A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation","abstract":"This study aims to reinforce the theoretical foundation for diverse systems--including the axiomatic definition of intelligence--by introducing a mathematically rigorous and unified formal structure for the concept of 'state,' which has long been used without consensus or formal clarity. First, a 'hierarchical state grid' composed of two axes--state depth and mapping hierarchy--is proposed to provide a unified notational system applicable across mathematical, physical, and linguistic domains. Next, the 'Intermediate Meta-Universe (IMU)' is introduced to enable explicit descriptions of definers (ourselves) and the languages we use, thereby allowing conscious meta-level operations while avoiding self-reference and logical inconsistency. Building on this meta-theoretical foundation, this study expands inter-universal theory beyond mathematics to include linguistic translation and agent integration, introducing the conceptual division between macrocosm-inter-universal and microcosm-inter-universal operations for broader expressivity. Through these contributions, this paper presents a meta-formal logical framework--grounded in the principle of definition = state--that spans time, language, agents, and operations, providing a mathematically robust foundation applicable to the definition of intelligence, formal logic, and scientific theory at large.","short_abstract":"This study aims to reinforce the theoretical foundation for diverse systems--including the axiomatic definition of intelligence--by introducing a mathematically rigorous and unified formal structure for the concept of 'state,' which has long been used without consensus or formal clarity. First, a 'hierarchical state gr...","url_abs":"https://arxiv.org/abs/2508.00853","url_pdf":"https://arxiv.org/pdf/2508.00853v1","authors":"[\"Kei Itoh\"]","published":"2025-07-14T11:37:35Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"cs.LO\"]","methods":"[]","has_code":false}