A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918111429525504 |
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| author | Itoh, Kei |
| author_facet | Itoh, Kei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation Itoh, Kei Artificial Intelligence Logic in Computer Science 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. |
| title | A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation |
| topic | Artificial Intelligence Logic in Computer Science |
| url | https://arxiv.org/abs/2508.00853 |