Hypergendered Logic Source
Hypergendered Logic — Page 178
Appendix T — Formal stage-relative modal semantics T.1 Model structure A metaexpressive HGL model can be represented as M = <B,H,E,W,Γ,V>, with separate female-side and male-side stage-indexed Γ functions. B is biological state, H is developmental history, E is environment/context, W is a family of admissible phenotype realization sets, and V evaluates phenotype propositions. T.2 Female accessibility relation w R^F_n v := v is a Γ^F_n-valid phenotype realization accessible from biological/context state w. w |= □^F_n φ iff for every v, w R^F_n v implies v |= φ. w |= ◇^F_n φ iff for some v, w R^F_n v and v |= φ. T.3 Male accessibility relation w R^M_n v := v is a Γ^M_n-valid phenotype realization accessible from biological/context state w. The female and male accessibility relations are structurally symmetric unless a specific HGL law introduces an asymmetry. T.4 Why the actual realization is accessible For a correctly classified valid subject, the actual phenotype world is one of the phenotype realizations licensed by the current Γ. This gives the stage modality its T/factivity behavior. T.5 No automatic S4/S5 The biological accessibility relation is not presumed transitive, symmetric, Euclidean, or reflexively introspective beyond the actual-validity condition. A body being able to reach phenotype v from phenotype w does not imply reverse reachability, and a phenotype possibility about another possibility is not automatically flattened. T.6 Modal equivalence versus phenotype equivalence Two subjects can share all currently observed phenotype propositions while differing in R_n and therefore differing in what they could express under counterfactual biological conditions. CurrentPhenotype(a)=CurrentPhenotype(b) does not imply R(a)=R(b). T.7 Fixed-address normality For each fixed valid Archaddress a, the adopted Kripke-style semantics is a normal address-relative modality. Therefore the K distribution law is valid: Box_a(phi -> psi) -> (Box_a(phi) -> Box_a(psi)). This is a logical property of the modality at one address, not a biological assertion that later stages preserve every possibility. T.8 Necessitation rule, narrowly typed If phi is a theorem valid in every world of the relevant model class, the normal modal rule permits inferring Box_a(phi). Necessitation does NOT license actual(phi) -> Box_a(phi), observed(phi) -> Box_a(phi), or possible(phi) -> Box_a(phi). A contingent biological truth does not become necessary merely because it actually occurs.
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:178.