Hypergendered Logic Source

Hypergendered Logic — Page 49

HGL Source Framework · Page 49 of 293 · Source: Hypergendered Logic

𝐼𝐻𝑆
( ),
it may infer and then . It must not add an IH(T) node unless inheritance of is separately stated or 
𝑆
𝑇
𝑇
derivable by an explicit inheritance law. 
66. Preserve PA irreducibility under IH 
The parser should represent 
 
𝐼𝐻𝑃𝐴𝑥∧¬𝑦
(
)
(
)
as an IH node whose child is one PA node whose child is one inner AND condition. It must never normalize 
this to two IH-of-PA nodes. 
67. Proof-trace every “therefore” 
Allowed proof labels should include: 
•​
classical conjunction elimination/introduction; 
•​
De Morgan; 
•​
double-negation elimination; 
•​
substitution of logically equivalent inner conditions where permitted; 
•​
PA irreducibility axiom; 
•​
IH projection; 
•​
no-provenance-lifting rule; 
•​
canonical SF/SM recursion; 
•​
FemaleType/MaleType axiom; 
•​
explicit causal law; 
•​
countermodel/non-entailment. 
If no rule can be named, the AI should mark the claim as inference, conjecture, or illustrative possibility 
rather than deduction. 
68. Store high stages as DAGs 
An AI should not textually expand SF1000 into every ancestor. Store symbolic nodes: 
SF[1000] -> IH(SF[999]) AND IH(NOT SM[999]) 
with recursive references. Memoize stage nodes and compute Boolean projections only when needed. 
This reduces computational duplication while preserving the inheritance genealogy exactly. 
69. Internal epistemic labels 
Every generated phenotype statement should carry one of: 
•​
LD — logical deduction; 
•​
LI — logical inference/conjecture; 
•​
CD — causal deduction under explicit causal law; 
•​
CI — causal inference; 
•​
EX — illustrative example; 
•​
OPEN — unresolved question. 
The final prose can be natural, but the reasoning system should retain the label so that “possible” is never 
accidentally rendered as “necessary.”

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:49.