Hypergendered Logic Source
Hypergendered Logic — Page 121
Forbidden: NOT ◇^F_n p The same partition applies on the male side. A rule can also be conditional, history-sensitive, tissue-sensitive, maturity-sensitive, or interaction-sensitive; the three basic statuses are the simplest modal classification. 235. Model-theoretic semantics Let W^F_n(B,H,E) be the nonempty set of phenotype realizations compatible with Γ^F_n for biological state B, developmental history H, and environment E. Let P_actual be the current realized phenotype. P_actual ∈ W^F_n(B,H,E). □^F_n φ iff for every P in W^F_n(B,H,E), P satisfies φ. ◇^F_n φ iff for some P in W^F_n(B,H,E), P satisfies φ. This semantics immediately explains why the Archstage meta-phenotype is global: Γ generates or constrains the admissible whole-body realization-space, while the elements of each realization can contain arbitrarily local traits. 236. Minimal modal laws adopted by HGL The stage-relative phenotype modality is treated as at least a normal, actual-world-valid biological modality. The following rules are safe under the model above. Duality: ◇_n p ↔ NOT □_n NOT p. K: □_n(p -> q) -> (□_n p -> □_n q). T/factivity: □_n p -> p, for a valid current Stage-n realization. Nonemptiness: □_n p -> ◇_n p. HGL does not automatically adopt S4, S5, symmetry, Euclideanness, or transitivity across biological phenotype worlds. Those frame properties would require biological justification. 237. Actuality implies biological possibility If a subject is a valid Stage-n Archfemale and actually expresses p, p must be among the realizations licensed by Γ^F_n. p_actual -> ◇^F_n p. This is a strict deduction only relative to the assumption that the observed subject is correctly classified and biologically valid under the stated Γ. If the observation appears to violate the modality, then at least one of the stage classification, phenotype observation, or Γ rule-set is wrong/incomplete. 238. Biological impossibility excludes actuality NOT ◇^F_n p -> NOT p_actual. This is stronger than saying p is unusual. It says p is outside the stage-valid expression-space. Again, the impossibility is stage-relative biological impossibility, not metaphysical impossibility. 239. Necessity versus mere possession PH(p-source) and □_n p answer different questions. PH can establish possession of a source-defined phenotype-profile. □_n p says every admissible current-stage realization has p. A trait can be actually possessed without being necessary across every admissible realization.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:121.