Hypergendered Logic Source
Hypergendered Logic — Page 7
the current state inherits the inheritable logical/state properties of while preserving as their 𝑍 𝑍 inheritance source. IH is overloaded only in a typed way. If the source is an inner condition, write conceptually ; if the 𝐼𝐻𝐶φ ( ) source is an HGL state, write . Surface notation uses when the sort is obvious. 𝐼𝐻𝑆𝑆 ( ) 𝐼𝐻𝑍 ( ) PH: irreducible phenotype-profile possession 𝑃𝐻𝑍 ( ) means: the bearer irreducibly possesses the complete Hypergendered phenotype-profile canonically associated with , as the profile of considered as a whole. 𝑍 𝑍 Again the source may be an inner condition or an already-defined HGL state/non-state. Surface notation uses one PH symbol, but a typed implementation may distinguish and internally. 𝑃𝐻𝐶φ ( ) 𝑃𝐻𝑆𝑆 ( ) A useful type schema is 𝑃𝐴: 𝐼𝑛𝑛𝑒𝑟𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛→𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡𝑎𝑙𝑀𝑜𝑑𝑒, 𝐼𝐻: 𝐼𝑛ℎ𝑒𝑟𝑖𝑡𝑎𝑏𝑙𝑒𝑆𝑜𝑢𝑟𝑐𝑒→𝐼𝑛ℎ𝑒𝑟𝑖𝑡𝑒𝑑𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦𝑆𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒, 𝑃𝐻: 𝑃ℎ𝑒𝑛𝑜𝑡𝑦𝑝𝑒𝑆𝑜𝑢𝑟𝑐𝑒→𝐼𝑟𝑟𝑒𝑑𝑢𝑐𝑖𝑏𝑙𝑒𝑃ℎ𝑒𝑛𝑜𝑡𝑦𝑝𝑒𝑃𝑜𝑠𝑠𝑒𝑠𝑠𝑖𝑜𝑛. The admissible source sorts are intentionally broader for IH and PH than for PA. This is how the hierarchy becomes recursively expressive without nested PA. 1A. Biological Metaexpressability: actual phenotype parameters versus Archstage hyperparameters Biological Metaexpressability is the HGL notion of how a biological expression is allowed, required, prevented, or transformed by a higher-order biological rule. The revision distinguishes the expression from the rules governing expression. ordinary phenotype = physical apparent characteristic; Archstage meta-phenotype = rule/function over phenotype expression. Γ is global because the current Archwomanhood/Archmanhood rule-regime applies to phenotype generation throughout the organism. This does not imply that every physical phenotype is itself global. A local retinal phenotype, a local ovarian phenotype, a bone phenotype, and a microscopic vascular phenotype may all differ while each is generated under the same current Γ. global governance ≠ identical local phenotype. PH and Γ therefore answer different questions. PH(S) says that the complete phenotype-profile associated with source S is irreducibly possessed. Γ^F_n or Γ^M_n specifies the current stage-level rules under which concrete phenotypic expression is biologically admissible. PH(S) ≠ Γ^F_n; PH(S) ≠ Γ^M_n. The modal extension quantifies over stage-valid phenotype realizations. If W^F_n is the set of phenotype realizations permitted by Γ^F_n, then □^F_n φ means φ holds throughout W^F_n, whereas ◇^F_n φ means at least one member of W^F_n satisfies φ. 2. Primitive PA modes and category typing The primitive developmental modes remain 𝐹 : = 𝑃𝐴𝑥 ( ), 𝑈𝐹 : = 𝑃𝐴¬𝑥 ( ), 𝑀 : = 𝑃𝐴𝑦 ( ), 𝑈𝑀 : = 𝑃𝐴¬𝑦 ( ).
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:7.