Hypergendered Logic Source

Hypergendered Logic — Page 10

HGL Source Framework · Page 10 of 293 · Source: Hypergendered Logic

PH(¬Z) is positive possession of the phenotype-profile associated with the logical non- source. ¬PH(Z) 
𝑍
merely says the profile is not fully possessed. 
𝑍
PH is not PA 
 
𝑃𝐻¬𝑥
(
)≢𝑃𝐴¬𝑥
(
).
PA(¬x) concerns developmental causation/availability. PH(¬x) concerns actual irreducible 
phenotype-profile possession. 
PH is not IH 
 
𝑃𝐻𝑍
( )≢𝐼𝐻𝑍
( ).
An inherited state may be present without the bearer yet possessing the entire phenotype-profile of that 
source, and a phenotype-profile can in principle be possessed without proving it was inherited from the 
source named by IH. The operators encode different facts. 
6. Logical equivalence inside PA/PH versus operator distribution 
Classical logic still applies to the Boolean formula occurring inside an operator when HGL permits 
substitution of logical equivalents. 
For example, 
 
¬ ¬𝑥∧𝑦
(
) ≡𝑥∨¬𝑦.
Therefore the source descriptions 
 
𝑃𝐻¬ ¬𝑥∧𝑦
(
)
(
)
and 
 
𝑃𝐻𝑥∨¬𝑦
(
)
may be treated as Boolean-normalized descriptions of the same source content while retaining provenance 
metadata. 
This does not license 
 
𝑃𝐻𝑥∨¬𝑦
(
) ≡𝑃𝐻𝑥
( ) ∨𝑃𝐻¬𝑦
(
).
Substitution of equivalents inside one source and distribution of an operator over source components are 
completely different operations. 
7. Seven scope distinctions that must not be conflated 
The current HGL grammar requires at least these constructions: 
1.​
inner negation 
; 
¬φ
2.​
outer state negation 
; 
¬𝑆
3.​
PA of negated condition 
; 
𝑃𝐴¬φ
(
)
4.​
positive inheritance 
; 
𝐼𝐻𝑍
( )
5.​
inheritance of a non-state 
; 
𝐼𝐻¬𝑆
(
)
6.​
phenotype possession 
; 
𝑃𝐻𝑍
( )
7.​
phenotype possession of a non-source 
. 
𝑃𝐻¬𝑍
(
)
Core nonidentities include 
 
𝑃𝐴¬φ
(
)≢¬𝑃𝐴φ
( ),
 
𝐼𝐻¬𝑍
(
)≢¬𝐼𝐻𝑍
( ),

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:10.