semanticChangeCount
The theorem states that the set of semantic change types under the J-cost model has exactly five elements. Linguists modeling historical meaning shifts via recognition ratios would cite this count to enumerate drift directions. The proof is a direct decision procedure that computes the cardinality from the finite inductive enumeration.
claimThe finite set of semantic change types has cardinality five: $|S| = 5$ where $S = $ {broadening, narrowing, amelioration, pejoration, metaphorical extension}.
background
In the Recognition Science treatment of linguistics, semantic change is driven by the J-cost of the recognition ratio r between a word's current and original meanings. Drift accumulates as J(r) grows across generations, with loss occurring once the ratio crosses the canonical J(phi) threshold. The module identifies five canonical types of semantic change that match the configuration dimension D = 5.
proof idea
The proof is a one-line wrapper that applies the decide tactic to compute the cardinality directly from the inductive definition of SemanticChangeType.
why it matters in Recognition Science
This result populates the five_types field inside semanticChangeCert, completing the enumeration required by the linguistics module. It instantiates the framework claim that semantic change types number five, matching configDim D = 5. No open questions are flagged in the supplied material.
scope and limits
- Does not derive explicit J-cost values for any change type.
- Does not specify the numerical threshold for semantic loss.
- Does not address rates of drift across generations.
- Does not extend the classification beyond the five listed types.
formal statement (Lean)
27theorem semanticChangeCount : Fintype.card SemanticChangeType = 5 := by decide
proof body
28