Hypergendered Logic Source

Hypergendered Logic — Page 36

HGL Source Framework · Page 36 of 293 · Source: Hypergendered Logic

Proposition 15 — Each higher female stage excludes the corresponding preceding 
male stage 
From 
SF^(n+1) = IH(SF^n) AND IH(NOT SM^n) AND PH(SF^n) AND NOT PH(SM^n) AND UD(SF^n) AND NOT 
FD(SF^n), for n >= 2 
we derive 
SFn+1⇒¬SMn. 
The male mirror is 
SMn+1⇒¬SFn. 
Proposition 16 — Opposite-side exclusion accumulates as a logical shadow 
By Proposition 15 and the base Stage-2 result, 
SFn⇒⋀n−1k=1¬HMk 
and 
SMn⇒⋀n−1k=1¬HFk. 
This is a statement about projected truth. It does not collapse distinct inherited source terms such as 
IH¬SM1 and IH¬SM7. 
Proposition 17 — IH cannot be lifted along arbitrary entailment 
Suppose 
. From 
, projection yields , then ordinary modus ponens yields . But nothing thereby 
𝑆⇒𝑇
𝐼𝐻𝑆
( )
𝑆
𝑇
establishes that was inherited from source . Hence 
𝑇
𝑇
 
𝐼𝐻𝑆
( ),  𝑆⇒𝑇 ⊭ 𝐼𝐻𝑇
( )
under the canonical provenance semantics. 
This proposition is essential. Without it, every logical consequence of an inherited source would be 
incorrectly retagged as a separately inherited source, destroying the distinction between projection and 
genealogy. 
Proposition 18 — IH does not destroy PA irreducibility 
If 
 
𝑆= 𝑃𝐴𝐴∧𝐵
(
),
then 
 inherits that exact irreducibly joint mode. Since PA distribution is invalid, we cannot infer 
𝐼𝐻𝑆
( )
 
𝐼𝐻𝑃𝐴𝐴
( )
(
) ∧𝐼𝐻𝑃𝐴𝐵
( )
(
).
Therefore 
 
𝐼𝐻𝑃𝐴𝐴∧𝐵
(
)
(
)≢𝐼𝐻𝑃𝐴𝐴
( )
(
) ∧𝐼𝐻𝑃𝐴𝐵
( )
(
)
as a general HGL rule. 
Proposition 19 — Nested inheritance increases full HGL depth 
Define

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:36.