A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation
Kei Itoh

TL;DR
This paper develops a rigorous, hierarchical formal framework for the concept of 'state' applicable across disciplines, introducing the Intermediate Meta-Universe for explicit meta-level descriptions and expanding inter-universal theory.
Contribution
It introduces a unified hierarchical state grid and the Intermediate Meta-Universe, enabling explicit meta-level descriptions and broadening inter-universal theory beyond mathematics.
Findings
Proposes a hierarchical state grid for unified notation.
Introduces the Intermediate Meta-Universe for meta-level operations.
Expands inter-universal theory to include linguistic and agent interactions.
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…
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Taxonomy
TopicsPhilosophy and History of Science · Origins and Evolution of Life · Embodied and Extended Cognition
