LogicSystem

formal source

  57  energy : State → ℝ
  58
  59/-- A logic system (simplified). -/
  60structure LogicSystem where
  61  /-- Propositions. -/
  62  Prop' : Type
  63  /-- Provability. -/
  64  proves : Prop' → Prop' → Prop
  65
  66/-- A qualia space (simplified). -/
  67structure QualiaSpace where
  68  /-- Experience states. -/
  69  State : Type
  70  /-- Valence (pleasure-pain axis). -/
  71  valence : State → ℝ
  72
  73/-- Embedding of a structure into UniversalStructure. -/
  74structure Embeds (T : Type) (R : UniversalStructure) where
  75  /-- The embedding map. -/
  76  embed : T → R.State
  77  /-- The map preserves structure: for now, we only require the map exists.
  78      Future work: formalize structure preservation via recognition/strain. -/
  79  structure_preserved : embed = embed  -- Reflexivity ensures embed is well-defined
  80
  81/-! ## The Universal Structure (Concrete) -/
  82
  83/-- Construct the universal structure. -/
  84def universalStructure : UniversalStructure := {
  85  State := ℝ,  -- Real numbers as universal state space
  86  recognizes := fun x y => x = y,  -- Identity recognition
  87  has_self_recognition := ⟨0, rfl⟩,
  88  strain := fun x => x^2,  -- Quadratic strain
  89  strain_nonneg := fun x => sq_nonneg x,
  90}