Hypergendered Logic Source

Hypergendered Logic — Page 149

HGL Source Framework · Page 149 of 293 · Source: Hypergendered Logic

A.8 Exact-stage interpretation 
For finite stages, 
ExactSFn=SFn∧¬SFn+1, 
ExactSMn=SMn∧¬SMn+1. 
Because full inheritance depth strictly differs, SFn and SFn+1 are not the same full HGL state even if some 
projected consequences overlap. 
A.9 Consistency versus opposition 
HGL does not need a general rule saying every pair 
 and 
 is contradictory as PA modes. What 
𝑃𝐴φ
( )
𝑃𝐴¬φ
(
)
is contradictory at the inner condition level is 
. Whether two outer PA states can coexist is a separate 
φ ∧¬φ
semantic question unless a causal consistency law links them. 
The current higher recursion avoids depending on such a general outer consistency axiom: it explicitly 
includes inherited non-opposite-stage states. 
A.10 Type semantics 
FemaleType and MaleType classify whole HGL states. They are not reducible to one PA atom. This 
permits 
FemaleTypeSF1 
while preserving 
SF1⇏PAx 
under general PA logic. 
Appendix B — De Morgan and scope drills under PA, IH, and PH 
B.1 Inner conjunction 
 
¬ 𝐴∧𝐵
(
) ≡¬𝐴∨¬𝐵.
Therefore 
 
𝑃𝐴¬ 𝐴∧𝐵
(
)
(
) ≡𝑃𝐴¬𝐴∨¬𝐵
(
)
if inner logical equivalents are substitutable. 
Do not continue to 
 
𝑃𝐴¬𝐴
(
) ∨𝑃𝐴¬𝐵
(
).
B.2 Inner disjunction 
 
𝑃𝐴¬ 𝐴∨𝐵
(
)
(
) ≡𝑃𝐴¬𝐴∧¬𝐵
(
).
Do not distribute PA. 
B.3 Outer PA conjunction 
 
¬ 𝑃𝐴𝐴
( ) ∧𝑃𝐴𝐵
( )
(
) ≡¬𝑃𝐴𝐴
( ) ∨¬𝑃𝐴𝐵
( ).
Do not rewrite the outputs as 
 or 
. 
𝑃𝐴¬𝐴
(
)
𝑃𝐴¬𝐵
(
)

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:149.