Toward an Ontology-Based Theory of Linguistic Transformation: Structural Entropy, Transformation Distance, and Inverse Control

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This paper proposes a theoretical framework for representing diverse linguistic paraphrases through ontology-based relations and inference paths. It distinguishes four constructs: a mapping from admissible textual expressions to structural states, state-conditioned structural entropy, transformation distance between an original item and its paraphrase, and a figure of merit (FoM) derived from structural observables. Under constraints of semantic preservation, answer validity, and construct preservation, selecting permissible transformations to approach a target structural state is formulated as an inverse problem. The multiplicity of realizations in statistical mechanics, relational composition in knowledge representation, and reachability in control theory serve as formal tools and analogies, without implying that linguistic expressions are physical microstates or that structural entropy directly determines psychometric difficulty. The contribution is a set of explicit conceptual distinctions, mathematical definitions, and testable research propositions rather than a claim of empirically validated difficulty control. Relationships between structural measurements and response-based item difficulty, as well as the stability of repeated generation and independent structural reading, remain questions for future empirical investigation.