IndisputableMonolith.Foundation.PreLogicalCost
PreLogicalCost defines pre-logical configuration values constrained to the unit interval as the starting point for cost-based emergence of logic. Researchers tracing the derivation of logical consistency from minimization would cite this module for its PreState and preCost primitives. The module supplies only definitions and is imported directly by LogicFromCost.
claimPre-logical configuration values are real numbers $c$ satisfying $0 \leq c \leq 1$.
background
The module sits in the Foundation domain and imports only Mathlib. Its doc-comment states that it treats pre-logical configuration values constrained to the unit interval. Sibling definitions include PreState, preCost, IsStable, stable_iff_boundary, StableState, band, bor, bnot and stable_forms_boolean_algebra, which together equip configurations with a cost function and basic stability and boolean structure before any logical axioms are introduced.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the pre-logical primitives required by LogicFromCost, whose doc-comment states that it proves logical consistency is a cost-minimizing state. It therefore occupies the initial position in the cost-to-logic derivation within the Recognition framework.
scope and limits
- Does not contain theorems or proofs.
- Does not import other Recognition modules.
- Does not address full logical consistency.
- Does not extend costs outside the unit interval.