Hypergendered Logic Source

Hypergendered Logic — Page 45

HGL Source Framework · Page 45 of 293 · Source: Hypergendered Logic

Thus SF3⇒SF2 and SF3⇒¬SM2. 
Status: deduction. 
Worked Example 11 — SF3 reaches SF1 transitively 
SF3⇒SF2⇒SF1. 
Status: deduction. 
Worked Example 12 — SM3 mirror 
SM3⇒SM2⇒SM1, 
and 
SM3⇒¬SF2. 
Status: deduction. 
Worked Example 13 — Do not distribute IH over a De Morgan disjunction 
From 
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) 
where the nine placeholders stand for the eight outer-negated Stage-2 conjuncts. IH(NOT SM2) may use a 
logically equivalent eight-disjunct source description if equivalent source descriptions are allowed. It may not 
be distributed into nine independent IH nodes without a new distribution axiom. 
 
𝐼𝐻𝐴
( ) ∨𝐼𝐻𝐵
( ) ∨𝐼𝐻𝐶
( ) ∨𝐼𝐻𝐷
( ) ∨𝐼𝐻𝐸
( ) ∨𝐼𝐻𝐹
( )
without a new distribution axiom. 
Status: anti-collapse rule. 
Worked Example 14 — Entailment does not retag inheritance 
Suppose SM5⇒SM2. From IHSM5 we can derive SM2 by projection and implication, but we cannot infer 
IHSM2 merely from those steps. 
Status: strict provenance rule. 
Worked Example 15 — IH preserves irreducible PA scope 
 
𝐼𝐻𝑃𝐴𝑥∧¬𝑦
(
)
(
)
inherits the joint PA mode. It does not imply separately inherited 
 and 
 routes. 
𝑃𝐴𝑥
( )
𝑃𝐴¬𝑦
(
)
Status: PA irreducibility + inheritance preservation. 
Worked Example 16 — Why SF2 explicitly adds 
 
𝑃𝐴𝑥
( )
Although SF1 contains inner x∧¬y, PA irreducibility does not give standalone PAx. Therefore writing PAx 
explicitly in SF2 introduces a distinct developmental mode. 
Status: strict HGL reasoning.

Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:45.