Hypergendered Logic Source

Hypergendered Logic — Page 9

HGL Source Framework · Page 9 of 293 · Source: Hypergendered Logic

Negation scope remains significant: 
 
𝐼𝐻¬𝑍
(
)≢¬𝐼𝐻𝑍
( ).
IH(¬Z) positively states inheritance from the non- source. ¬IH(Z) merely denies that is inherited. 
𝑍
𝑍
IH preserves causal scope. If 
 
𝑍= 𝑃𝐴𝐴∧𝐵
(
),
then 
 
𝐼𝐻𝑍
( )
inherits the irreducibly joint PA mode. It does not split into separately inherited 
 and 
 modes. 
𝑃𝐴𝐴
( )
𝑃𝐴𝐵
( )
IH also preserves source identity and nesting depth. Thus 
 
𝐼𝐻𝐼𝐻𝑍
( )
(
)
projects to 
 and then to , but its full inheritance identity is not flattened to 
. 
𝐼𝐻𝑍
( )
𝑍
𝐼𝐻𝑍
( )
Condition-source IH versus state-source IH 
Earlier editions placed condition-source IH terms in Stage 1. The corrected Stage-1 definitions do not: SF1 
and SM1 are PA-only. Condition-source IH remains a legal operator form in HGL generally, but it is not 
constitutive of canonical SF1/SM1. 
This gives another anti-collapse rule: 
 
𝐼𝐻𝑥
( )≢𝑃𝐴𝑥
( ).
Projection from 
 yields the condition ; it does not create a standalone PA route. 
𝐼𝐻𝑥
( )
𝑥
5. PH phenotype-profile irreducibility 
Let 
 denote the canonical Hypergendered phenotype-profile associated with source . Then 
Π 𝑍
( )
𝑍
 
𝑃𝐻𝑍
( )
means the bearer possesses the complete profile 
 as one irreducible -profile. 
Π 𝑍
( )
𝑍
This is stronger than merely possessing each visible trait in some accidental way. If 
 is explicitly 
τ ∈Π 𝑍
( )
established, then 
 
𝑃𝐻𝑍
( ) ⇒𝐻𝑎𝑠τ
( ).
But merely collecting all familiar-looking traits does not automatically establish 
 unless the 
𝑃𝐻𝑍
( )
whole-profile identity/provenance condition is met. 
PH does not distribute over compound sources 
 
𝑃𝐻𝐴∧𝐵
(
)≢𝑃𝐻𝐴
( ) ∧𝑃𝐻𝐵
( )
and 
 
𝑃𝐻𝐴∨𝐵
(
)≢𝑃𝐻𝐴
( ) ∨𝑃𝐻𝐵
( ).
A compound whole can have phenotype-properties that neither component profile has separately. 
PH negation scope 
 
𝑃𝐻¬𝑍
(
)≢¬𝑃𝐻𝑍
( ).

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:9.