SemanticChangeType
SemanticChangeType enumerates the five canonical categories of semantic shift in the Recognition Science model of historical linguistics. Linguists applying the J-cost functional to word-meaning evolution cite this enumeration to fix the configuration dimension at D=5. The declaration is a direct inductive definition that derives Fintype, which immediately supports the downstream cardinality theorem.
claimLet $T$ be the inductive type whose constructors are broadening, narrowing, amelioration, pejoration, and metaphoricalExtension. The type carries the derived instances DecidableEq, Repr, BEq, and Fintype.
background
In the Recognition Science treatment of historical linguistics, semantic drift is measured by the recognition ratio $r$ = current meaning / original meaning, with cost given by the J-functional $J(r)$. The module states that the canonical J(phi) threshold marks when a word is considered semantically lost. Five standard change types are identified and asserted to equal the configuration dimension D=5.
proof idea
The declaration is a direct inductive definition introducing five nullary constructors. The deriving clause automatically installs the DecidableEq, Repr, BEq, and Fintype instances; no further proof steps are required.
why it matters in Recognition Science
This definition supplies the five-type enumeration required by SemanticChangeCert (which pairs it with a CanonicalCert threshold) and by the theorem semanticChangeCount that proves Fintype.card SemanticChangeType = 5. It realizes the RS claim that semantic change types match configDim D=5 inside the J-cost framework.
scope and limits
- Does not model transition rates or mechanisms between the five types.
- Does not compute explicit J-cost values for each constructor.
- Does not incorporate empirical diachronic corpora or validation data.
formal statement (Lean)
23inductive SemanticChangeType where
24 | broadening | narrowing | amelioration | pejoration | metaphoricalExtension
25 deriving DecidableEq, Repr, BEq, Fintype
26