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Theoretical analysis demonstrates bidirectional abstraction in non-terminal world models, suggesting mechanisms for vocabulary revision during scientific discovery.
Scientific discovery sometimes requires more than selecting a better hypothesis within a fixed representational vocabulary: it requires revising the vocabulary itself. This preprint develops a theoretical framework for conceptual-revision abduction as a bidirectional search over representational commitments and abstraction depth. Observations, inherited knowledge, and the current world model generate ascending empirical constraints; reopened and progressively more general commitments generate descending reconstructions of candidate concrete world models. At each abstraction level, an agent seeks a model that satisfies both directions while recovering the regime in which the previous model succeeded. The paper defines abductive depth as the minimum abstraction depth - or, in the general case, minimum abstraction-path cost - at which such reconciliation becomes empirically adequate. It states structural results on fixed-representation reachability, the joint requirement for representational reopening and empirical discrimination under explicit assumptions, minimum-sufficient abstraction under monotone cost, and the limitations imposed by terminal explanatory commitments. The resulting concept of a non-terminal world model permits provisional stopping without granting irreversible explanatory privilege to current primitives. Complete symmetry is discussed only as an optional programmatic limiting reference for a future physical instantiation; it is not presented as an empirically established origin state or a required starting point for reasoning.
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浩平 野口 (2026) studied this question.
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