Hypergendered Logic Source

Hypergendered Logic — Page 15

HGL Source Framework · Page 15 of 293 · Source: Hypergendered Logic

Example 4: outer disjunction of states 
 
¬ 𝑃𝐴𝑥
( ) ∨𝑃𝐴𝑦
( )
(
) ≡¬𝑃𝐴𝑥
( ) ∧¬𝑃𝐴𝑦
( ).
Example 5: user-style double outer negation 
 
¬𝑃𝐴𝑥
( ) ∧¬𝑃𝐴¬𝑦
(
) ≡¬ 𝑃𝐴𝑥
( ) ∨𝑃𝐴¬𝑦
(
)
(
).
Example 6: three-term higher-state negation 
If 
 
𝑆𝑀
2 = 𝑃𝐴𝑦
( ) ∧𝑃𝐴¬𝑥∧𝑦
(
) ∧𝑃𝐴¬𝑥
(
),
then 
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) 
Example 7: inner simplification inside one term of Example 6 
The inner antithesis of 
 is 
𝑃𝐴¬𝑥∧𝑦
(
)
 
𝑃𝐴¬ ¬𝑥∧𝑦
(
)
(
) ≡𝑃𝐴𝑥∨¬𝑦
(
).
This is distinct from the outer term 
 
¬𝑃𝐴¬𝑥∧𝑦
(
).
Example 8: nested mixed formula 
Let 
 
𝑇= 𝑃𝐴¬ 𝑥∧¬𝑦
(
)
(
) ∨¬𝑃𝐴𝑦
( ).
The inner PA term simplifies to 
 
𝑃𝐴¬𝑥∨𝑦
(
),
so 
 
𝑇≡𝑃𝐴¬𝑥∨𝑦
(
) ∨¬𝑃𝐴𝑦
( ).
But no further collapse is justified unless additional HGL axioms connect 
 with 
. 
𝑃𝐴¬𝑥∨𝑦
(
)
¬𝑃𝐴𝑦
( )
Part IV — First-order Suprafemale and Supramale 
13. Canonical Suprafemale Stage 1 
The canonical first Suprafemale state is PA-only. It is not a five-part IH/PA/PH state and is not 
phenotype-enriched by constitutive PH terms. 
SF1 = PA(x AND NOT y) 
In full condition labels: SF1 = PA(XX AND NOT XY). 
SF1 therefore contains one constitutive developmental-causal mode: PA(x AND NOT y). The compound x 
AND NOT y remains one irreducible PA source. 
Strict deduction from the definition: SF1 entails PA(x AND NOT y). No condition-source IH term, PH term, UD 
term, or FD term is constitutive of SF1.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:15.