Hypergendered Logic Source
Hypergendered Logic — Page 147
Appendix A — Model-theoretic semantics for PA, IH, and PH A.1 Three kinds of identity A rigorous HGL model should distinguish at least three equivalence notions. Inner logical equivalence concerns condition formulas: φ≡𝐿ψ. For example, ¬ ¬𝑥∧𝑦 ( )≡𝐿𝑥∨¬𝑦. Boolean state equivalence concerns the ordinary truth projection of complete HGL states: 𝑆≡𝐵𝑇. Inheritance-sensitive identity preserves IH source and depth: 𝑆≡𝐼𝑇. The intended relationships are not total collapses. In particular, 𝑆≡𝐼𝑇⇒𝑆≡𝐵𝑇 is reasonable for exact state identity, but 𝑆≡𝐵𝑇 ⇏ 𝑆≡𝐼𝑇. Two states can have the same Boolean projection while differing in causal-developmental genealogy. A.2 A minimal semantic structure An HGL model can be represented schematically as 𝑀= ⟨𝑊, 𝑉, 𝑃, 𝐼, τ, Φ⟩, where: • is a set of possible biological/developmental worlds or states; 𝑊 • evaluates inner condition atoms such as and ; 𝑉 𝑥 𝑦 • interprets PA modes and remembers designated causal basis; 𝑃 • interprets inheritance edges and source identity; 𝐼 • assigns FemaleType/MaleType; τ • is a phenotype map. Φ The point of this structure is not to claim HGL has only one possible model theory. It demonstrates what information a semantics must preserve if it is to respect the current rules. A.3 PA as an intensional causal operator A simple extensional interpretation that maps every logically equivalent condition to the same developmental mode can preserve inner Boolean equivalence. But PA must also retain causal basis. Thus the model should not assume monotonicity: φ ⇒ψ does not force
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:147.