IndisputableMonolith.Cognition.AnalogicalReasoningFromJCost

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Analogical Reasoning from J-Cost — D3 Cognition Depth
   6
   7Analogy = structural mapping between two domains where recognition
   8patterns match. In RS terms, two structures A and B are analogous iff
   9their recognition cost structures satisfy J(r_A) ≈ J(r_B) for
  10corresponding recognition ratios.
  11
  12The canonical analogical depth: the closer J(r_A) - J(r_B) is to 0,
  13the stronger the analogy. Perfect analogy = J(r_A) = J(r_B).
  14
  15Five canonical analogy types (structural, functional, causal, semantic,
  16formal) = configDim D = 5.
  17
  18The J-symmetry theorem: J(r) = J(1/r) implies that inverse mappings
  19preserve analogical strength — a foundation for analogy-preservation.
  20
  21Lean status: 0 sorry, 0 axiom.
  22-/
  23
  24namespace IndisputableMonolith.Cognition.AnalogicalReasoningFromJCost
  25open Cost
  26
  27inductive AnalogyType where
  28  | structural | functional | causal | semantic | formal
  29  deriving DecidableEq, Repr, BEq, Fintype
  30
  31theorem analogyTypeCount : Fintype.card AnalogyType = 5 := by decide
  32
  33/-- Inverse mapping preserves J-cost (analogy-preservation). -/
  34theorem inverse_preserves_cost {r : ℝ} (hr : 0 < r) :
  35    Jcost r = Jcost r⁻¹ := Jcost_symm hr
  36
  37/-- Perfect analogy (r_A = r_B) implies zero cost difference. -/
  38theorem perfect_analogy_zero {r : ℝ} (hr : 0 < r) :
  39    Jcost r - Jcost r = 0 := sub_self _
  40
  41structure AnalogicalReasoningCert where
  42  five_types : Fintype.card AnalogyType = 5
  43  inverse_preserves : ∀ {r : ℝ}, 0 < r → Jcost r = Jcost r⁻¹
  44  perfect_zero : ∀ {r : ℝ}, 0 < r → Jcost r - Jcost r = 0
  45
  46def analogicalReasoningCert : AnalogicalReasoningCert where
  47  five_types := analogyTypeCount
  48  inverse_preserves := Jcost_symm
  49  perfect_zero := fun {r} _ => sub_self _
  50
  51end IndisputableMonolith.Cognition.AnalogicalReasoningFromJCost
  52