pith. sign in
module module moderate

IndisputableMonolith.CrossDomain.CognitiveStateSpace

show as:
view Lean formalization →

The CrossDomain.CognitiveStateSpace module defines the types Sense, Emotion, MemorySystem and their composition into CognitiveState together with the three projection maps. Researchers extending Recognition Science to cognitive modeling would cite these definitions when building state spaces on top of the J-cost and phi-ladder. The module consists of type declarations followed by surjectivity statements for each projection.

claimLet $S$, $E$, $M$ be the types Sense, Emotion, MemorySystem. Define CognitiveState with projections $\pi_S : \text{CognitiveState} \to S$, $\pi_E : \text{CognitiveState} \to E$, $\pi_M : \text{CognitiveState} \to M$ each surjective.

background

The module sits in the CrossDomain section and imports only Mathlib. It introduces Sense as the type of sensory configurations, Emotion as affective states, MemorySystem as storage structures, and CognitiveState as the joint object equipped with the three projections. The supplied doc-comment states that the sense projection is surjective; the sibling lemmas establish the same for the other two maps. This supplies the minimal state space before any dynamics or recognition rules are added.

proof idea

This is a definition module. It declares the four types, defines the projections, and states the three surjectivity lemmas (senseProj_surj and its siblings) directly from the type definitions.

why it matters in Recognition Science

The module supplies the CognitiveState type and its projections that any later cross-domain theorem on cognitive recognition would require. No downstream theorems are listed in the used_by block, so it currently stands as an interface definition for future work on cognitive extensions of the Recognition Composition Law.

scope and limits

declarations in this module (19)