module module high

`IndisputableMonolith.Philosophy.ModalOntologyStructure`

ModalOntologyStructure defines RS modal predicates by classifying entities according to J-cost and defect status. It imports LawOfExistence and OntologyPredicates to ground necessity as the unique J-minimizer with zero defect. The module supplies definitions for RSNecessary, RSPossible, RSActual, and RSImpossible along with basic properties such as uniqueness and positivity ratios. Researchers formalizing modality inside Recognition Science cite it to link ontology directly to cost minimization.

claim$RSNecessary(x) :⇔ x$ is the unique $J$-minimizer with $defect(x)=0$; $RSPossible(x)$, $RSActual(x)$, $RSImpossible(x)$ defined via positive $J$-cost ratios and non-positive costs.

background

LawOfExistence states that $x$ exists if and only if $defect(x)=0$. OntologyPredicates treats existence and truth as selection outcomes from minimization under the unique $J$ function. The module extends these foundations into modal ontology by defining necessity, possibility, actuality, and impossibility through J-cost properties and defect thresholds.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

This module feeds the Recognition Science philosophy domain by supplying modal ontology predicates that connect LawOfExistence to interpretations of necessity and possibility. It structures the predicates used in arguments about existence and truth under the J-cost framework.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Foundation.LawOfExistence module_import
IndisputableMonolith.Foundation.OntologyPredicates module_import

declarations in this module (21)

def RSNecessary L55
def RSPossible L58
def RSActual L61
def RSImpossible L64
theorem necessity_is_unique_minimizer L71
theorem necessary_is_one L81
theorem possibility_is_positive_ratio L91
theorem possible_has_finite_cost L96
theorem possibility_is_not_singleton L101
theorem actuality_is_j_minimum L110
theorem actuality_is_unique L121
theorem impossible_is_non_positive L129
theorem possible_not_impossible L138
theorem s5_necessity_implies_actuality L147
theorem s5_actuality_implies_possibility L154
theorem s5_possible_accessible_to_necessary L161
def modalDistance L170
theorem modal_distance_nonneg L173
theorem modal_distance_zero_iff_actual L178
theorem actual_has_zero_modal_distance L185
theorem ph013_modal_certificate L205