MemorySystem
MemorySystem enumerates five memory categories as an inductive type with automatic Fintype and decidable equality instances. Cognitive modelers cite it when forming the 125-element product CognitiveState from the three axes. The definition is a direct inductive enumeration whose derived Fintype instance supplies the cardinality 5 used in all downstream count and surjectivity theorems.
claimLet $M$ be the finite set with elements working, episodic, semantic, procedural, and priming, equipped with decidable equality and Fintype structure so that $|M|=5$.
background
The module constructs a cognitive state space as the product of three five-element axes: Sense, Emotion, and MemorySystem. Their Cartesian product is CognitiveState, whose cardinality is certified as 125. MemorySystem supplies the third axis via the five listed constructors. Module documentation states that the conscious moment is spanned by three orthogonal recognition axes each of dimension 5, so that Sense × Emotion × MemorySystem = 125; the Lean content records the enumerated structure under that decomposition.
proof idea
The declaration is the inductive definition itself, introducing the five constructors and deriving DecidableEq, Repr, BEq, Fintype. No separate proof body exists; the Fintype instance is used directly by the decide tactic in sibling theorems such as memorySystemCount.
why it matters in Recognition Science
MemorySystem is one factor in the abbrev CognitiveState and in the structure CognitiveStateSpaceCert, which records the product cardinality 125 together with surjective projections and the strict inequality against each factor. It realizes the structural claim of the C1 module for the 5³ state space and supplies the memory axis required by the non-collapse theorems notCollapsedToMemory and notCollapsedToPair2.
scope and limits
- Does not assert that the five memory categories are exhaustive for biological systems.
- Does not establish empirical independence of the three axes from neural data.
- Does not define transition rules or dynamics on the resulting 125 states.
- Does not claim that the labels correspond to any particular neural implementation.
formal statement (Lean)
35inductive MemorySystem where
36 | working | episodic | semantic | procedural | priming
37 deriving DecidableEq, Repr, BEq, Fintype
38