IndisputableMonolith.Cognition.AnalogicalReasoningFromJCost
This module formalizes analogical reasoning in cognition by showing that J-cost is preserved under inverse mappings. Researchers modeling cognition via Recognition Science would cite it to ground analogy formation in the cost function from the Cost module. The module supplies type definitions for analogies together with lemmas establishing cost invariance and zero cost for perfect cases.
claimLet $J$ denote the J-cost. An analogy type is a mapping $f$ such that $J(f(x)) = J(x)$ for the inverse $f^{-1}$, with perfect analogies satisfying $J=0$. The module certifies analogical reasoning when these preservation properties hold.
background
The module sits in the Cognition domain and imports the Cost module, which supplies the J-cost function $J(x) = (x + x^{-1})/2 - 1$. It introduces analogy types that count admissible mappings and certificates that witness cost-preserving analogies. The local setting extends Recognition Science by applying J-uniqueness to cognitive operations, treating analogy as an instance of cost invariance under inversion.
proof idea
This is a definition module. It declares the AnalogyType and AnalogicalReasoningCert objects, then supplies short lemmas that verify inverse preservation of J-cost and zero cost for perfect analogies.
why it matters in Recognition Science
The module supplies the basic objects needed to embed analogical reasoning inside the Recognition Science cost framework. It directly supports downstream cognition results that link J-cost preservation to higher-level inference steps in the forcing chain.
scope and limits
- Does not derive new values for physical constants.
- Does not prove existence of specific analogies in data.
- Does not connect to the phi-ladder mass formula.