Hypergendered Logic Source

Hypergendered Logic — Page 150

HGL Source Framework · Page 150 of 293 · Source: Hypergendered Logic

B.4 Outer IH conjunction 
 
¬ 𝐼𝐻𝑆
( ) ∧𝐼𝐻𝑇
( )
(
) ≡¬𝐼𝐻𝑆
( ) ∨¬𝐼𝐻𝑇
( ).
Do not rewrite to 
. 
𝐼𝐻¬𝑆
(
) ∨𝐼𝐻¬𝑇
(
)
B.5 Negating SF2 
SF2 = IH(SF1) AND IH(NOT SM1) AND PH(SF1) AND NOT PH(SM1) AND UD(SF1) AND PA(x) AND 
PA(NOT y) AND NOT FD(SF1) 
Hence 
NOT SF2 = NOT IH(SF1) OR NOT IH(NOT SM1) OR NOT PH(SF1) OR PH(SM1) OR NOT UD(SF1) OR 
NOT PA(x) OR NOT PA(NOT y) OR FD(SF1) 
B.6 Negating SM2 
NOT SM2 = NOT IH(SM1) OR NOT IH(NOT SF1) OR NOT PH(SM1) OR PH(SF1) OR NOT UD(SM1) OR 
NOT PA(NOT x) OR NOT PA(y) OR FD(SM1) 
B.7 SF3’s second source 
SF3 = IH(SF2) AND IH(NOT SM2) AND PH(SF2) AND NOT PH(SM2) AND UD(SF2) AND NOT FD(SF2) 
The source of the second IH can be normalized using B.6, but IH remains outside the entire normalized 
source formula. 
B.8 Double negation inside PA 
 
𝑃𝐴¬¬𝑥
(
) ≡𝑃𝐴𝑥
( )
under classical double-negation equivalence of inner conditions. 
B.9 Double outer negation 
 
¬¬𝑃𝐴𝑥
( ) ≡𝑃𝐴𝑥
( ).
This is different from moving NOT through PA. 
B.10 Double outer negation around IH 
 
¬¬𝐼𝐻𝑆
( ) ≡𝐼𝐻𝑆
( ).
Again, this does not flatten the IH node. 
B.11 IH of an inner-antithetical PA mode 
 
𝐼𝐻𝑃𝐴¬𝑥
(
)
(
)
means inherit the Unfemale PA mode. It is different from 
 
𝐼𝐻¬𝑃𝐴𝑥
( )
(
),
which inherits the outer non-Female-mode state. 
B.12 Four nested scopes 
Consider 
 
¬𝐼𝐻¬𝑃𝐴𝑥∧¬𝑦
(
)
(
).
Read from inside outward:

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:150.