IndisputableMonolith.Foundation.LogicFromCost
The LogicFromCost module introduces PropConfig as the basic unit for propositional logic derived from cost functions in Recognition Science. A PropConfig pairs a proposition with a positive real ratio that encodes its stability and truth value, with ratio 1 for balanced true statements. It relies on upstream modules establishing existence via zero defect and truth via cost minimization under the J function. This setup allows logic to emerge from pre-logical cost constraints without assuming classical truth values a priori. The module contains a
claimA propositional configuration is a pair $(P, r)$ where $P$ is a proposition and $r > 0$ is its ratio state, with $r = 1$ for perfectly balanced true propositions, $r$ near 0 for absent false propositions, and $r$ large for unstable assertions.
background
Recognition Science derives logic from a cost function J satisfying the Recognition Composition Law. Upstream, the Law of Existence states that x exists if and only if its defect is zero. The OntologyPredicates module defines RSExists and RSTrue as outcomes of cost minimization under the unique J function. PreLogicalCost constrains configuration values to the unit interval. This module defines PropConfig to extend these ideas to propositions, assigning each a ratio state that measures balance.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the core definitions for building logical structures from cost in the Recognition Science framework. It directly supports sibling declarations such as IsLogicalContradiction and ConsistentConfig, which handle contradictions and consistency via cost. It fills the step from pre-logical costs to propositional logic, connecting to the Law of Existence by ensuring propositions with zero defect are stable at ratio 1.
scope and limits
- Does not derive the full set of logical connectives.
- Does not prove any theorems about the J function.
- Does not address higher-dimensional or physical interpretations.
- Does not include numerical computations or examples.
depends on (3)
declarations in this module (19)
-
structure
PropConfig -
def
prop_cost -
def
IsStable -
def
IsUnstable -
structure
ContradictionConfig -
def
contradiction_cost -
theorem
contradiction_positive_cost -
def
IsLogicalContradiction -
theorem
logical_contradiction_impossible -
theorem
zero_cost_contradiction_forbidden -
structure
ConsistentConfig -
def
consistent_cost -
theorem
consistent_zero_cost_possible -
theorem
consistent_minimum_cost -
theorem
logic_from_cost -
theorem
why_logic_is_real -
theorem
prelogical_boolean_fragment -
theorem
mp_from_cost_and_logic -
theorem
logic_from_cost_summary