Hypergendered Logic Source

Hypergendered Logic — Page 8

HGL Source Framework · Page 8 of 293 · Source: Hypergendered Logic

Unfemale is not merely not-Female: 
 
𝑃𝐴¬𝑥
(
)≢¬𝑃𝐴𝑥
( ).
Unmale is not merely not-Male: 
 
𝑃𝐴¬𝑦
(
)≢¬𝑃𝐴𝑦
( ).
The type predicates remain separate from any single PA route: 
FemaleTypeSFn,  MaleTypeSMn n≥1. 
This protects the sex-category invariant without forcing PA monotonicity. 
3. PA Irreducibility 
The canonical example is 
 
𝑃𝐴𝑥∧¬𝑦
(
).
Its reading is: 
physiology and anatomy necessarily developable irreducibly both due to XX presence and XY 
absence together. 
Therefore 
 
𝑃𝐴𝑥∧¬𝑦
(
)≢𝑃𝐴𝑥
( ) ∧𝑃𝐴¬𝑦
(
).
Although 
 
𝑥∧¬𝑦⇒𝑥
and 
 
𝑥∧¬𝑦⇒¬𝑦,
HGL rejects unrestricted causal lifting: 
 
𝑃𝐴𝑥∧¬𝑦
(
) ⇏ 𝑃𝐴𝑥
( )
and 
 
𝑃𝐴𝑥∧¬𝑦
(
) ⇏ 𝑃𝐴¬𝑦
(
)
as general laws. 
The same principle applies to disjunction: 
 
𝑃𝐴𝐴∨𝐵
(
)≢𝑃𝐴𝐴
( ) ∨𝑃𝐴𝐵
( ).
Logical decomposition of an inner condition is not causal decomposition of a PA mode. 
4. IH inheritance laws 
The primary projection rule is 
 
𝐼𝐻𝑍
( ) ⇒𝑍.
The converse is not generally valid: 
 
𝑍 ⇏ 𝐼𝐻𝑍
( ).
Inheritance is therefore more informative than mere possession.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:8.