Hypergendered Logic Source

Hypergendered Logic — Page 174

HGL Source Framework · Page 174 of 293 · Source: Hypergendered Logic

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automatic IH flattening. 
P.8b Limit-stage and transordinal conformance tests 
· A limit ordinal lambda must denote a constructed LimF/LimM stage before Q(SF^lambda) or Q(SM^lambda) 
may be used. 
· Do not treat the finite-only metavariable n in an old successor formula as sufficient syntax for omega+1. 
The authoritative successor schema is ordinal-general for every already-defined ordinal alpha >= 2. 
· A limit stage must expose predecessor-closure consequences for every beta<lambda while preserving beta 
as the source index. 
· Do not require a literal infinitary object-language conjunction; the canonical implementation uses a typed 
set-indexed Limit-State Closure Constructor. 
· Limit closure inherits every same-side predecessor and every structured opposite nonstate; positively 
possesses every same-side predecessor profile; excludes every complete opposite predecessor profile; 
makes every same-side predecessor an Unflaw; and asserts NOT-FD for every same-side predecessor. It 
does not constitutively assign PH(NOT opposite), UD(opposite nonstate), or any FD status to the opposite 
source. 
· Significant Quality Increase is magnitude-crossing at finite and transfinite levels; within-magnitude 
improvement is not SQI even if numerically or physically large. 
· Keep address-cardinality, IH-depth ordinal, and quality-magnitude cardinality as separate typed quantities. 
P.9 Biological Metaexpression and modal conformance tests 
Test M1. Input: local phenotype p under valid Γ^F_5. Expected: global Γ does not force p to occur in every 
tissue. 
Test M2. Input: p is actually expressed at valid Stage 5. Expected: infer ◇^F_5 p. 
Test M3. Input: □^F_5 p. Expected: infer p in the valid current realization. 
Test M4. Input: NOT ◇^F_5 p. Expected: infer NOT p in any valid Stage-5 realization. 
Test M5. Input: ◇^F_5 p. Expected: do not infer p. 
Test M6. Input: p. Expected: do not infer □^F_5 p. 
Test M7. Input: ◇^F_5 p. Expected: do not infer ◇^F_6 p without a cross-stage rule. 
Test M8. Input: PH(SF5). Expected: do not rewrite as Γ^F_5. 
Test M9. Input: Γ^F_5 constant while θ changes. Expected: phenotype may change without Stage 6. 
Test M10. Input: PA(NOT((x AND NOT y) OR ψ)). Expected: accept as one PA node with nested logical 
source. 
Test M11. Input: PA(PA(x)). Expected: reject as noncanonical nested-PA type. 
Test M12. Input: NOT □_n p. Expected: do not rewrite as □_n NOT p. 
Test M13. Input: NOT ◇_n p. Expected: permit normalization to □_n NOT p under adopted dual semantics. 
Test M14. Input: same visible phenotype at SF4 and SF20. Expected: do not infer equal Γ or equal modal 
phenotype-space. 
Test M15. Input: same Γ at two ages. Expected: do not infer same actual phenotype. 
Appendix Q — Canonical reference for direct implementation 
CONDITION LANGUAGE​
 x := XX​
 y := XY​
 phi ::= x | y | NOT phi | (phi AND phi) | (phi OR phi)​
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PA​
 PA(phi) := physiology/anatomy necessarily developable due to phi as one designated causal basis​
 PA(compound phi) is irreducible and does not generally distribute​
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Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:174.