Hypergendered Logic Source

Hypergendered Logic — Page 158

HGL Source Framework · Page 158 of 293 · Source: Hypergendered Logic

Appendix G — Short-form canonical reference sheet 
G.1 Symbols 
 
𝑥= 𝑋𝑋,   𝑦= 𝑋𝑌.
G.2 Primitive PA modes 
 
𝐹= 𝑃𝐴𝑥
( ),  𝑈𝐹= 𝑃𝐴¬𝑥
(
),  𝑀= 𝑃𝐴𝑦
( ),  𝑈𝑀= 𝑃𝐴¬𝑦
(
).
G.3 First order 
SF1 = PA(x AND NOT y) 
SM1 = PA(NOT x AND y) 
G.4 Second order 
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) 
SM2 = IH(SM1) AND IH(NOT SF1) AND PH(SM1) AND NOT PH(SF1) AND UD(SM1) AND PA(NOT x) AND 
PA(y) AND NOT FD(SM1) 
G.5 Higher order 
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 
SM^(alpha+1) = IH(SM^alpha) AND IH(NOT SF^alpha) AND PH(SM^alpha) AND NOT PH(SF^alpha) AND 
UD(SM^alpha) AND NOT FD(SM^alpha), for every defined ordinal alpha >= 2 
G.6 PA rules 
 
𝑃𝐴¬𝑝
(
)≢¬𝑃𝐴𝑝
( ),
 
𝑃𝐴𝐴∧𝐵
(
)≢𝑃𝐴𝐴
( ) ∧𝑃𝐴𝐵
( ),
 
𝑃𝐴𝐴∨𝐵
(
)≢𝑃𝐴𝐴
( ) ∨𝑃𝐴𝐵
( ).
G.7 IH rules 
 
𝐼𝐻𝑆
( ) ⇒𝑆,
 
𝑆 ⇏ 𝐼𝐻𝑆
( ),
 
𝐼𝐻¬𝑆
(
)≢¬𝐼𝐻𝑆
( ),
 
𝐼𝐻𝐼𝐻𝑆
( )
(
)≢𝐼𝐼𝐻𝑆
( ).
No general IH distribution or entailment-to-IH lifting. 
G.8 Type rules 
FemaleTypeSFn,  MaleTypeSMn. 
G.9 Depth 
dIHstageSFn=dIHstageSMn=n−1. 
G.10 Developmental separation 
 
∆𝑠𝑡𝑎𝑔𝑒= 0 ⇏ ∆𝑤𝑜𝑚𝑎𝑛/𝑚𝑎𝑛 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡= 0.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:158.