nx_classical.nx
buildroot/runtime/nx_classical.nx
about
nx_classical.nx -- classical-logic axioms.
Closes the named blocker for nonconstructive proofs (currently
PARTIAL in the audit). Per user 2026-05-15: "no losses".
Adds two axioms that are sound in CLASSICAL but not INTUITIONISTIC
logic. The kernel core (nx_kernel_v2) stays intuitionistic;
classical proofs explicitly cite these axioms so the audit trail
always shows whether classical logic was used.
LEM: for any A, A | ~A
DNE: for any A, ~~A => A
LEM and DNE are interderivable in classical logic; we ship both
because each saves a step in different proof shapes. HOL Light
derives the rest from these (Peirce's law, RAA, etc.) via the
engine + the existing v2 rules.
dependencies 1 imports · 1 importers
imports: nx_kernel_v2.nx
imported by: nx_world_class_test.nx
structs
| none |
consts
| none |
functions
| 28 | func nx_classical_lem(ch: *K2Chain, a: *Term) -> nx_int |
| 33 | func nx_classical_dne(ch: *K2Chain, a: *Term) -> nx_int |
| 40 | func nx_classical_peirce(ch: *K2Chain, a: *Term, b: *Term) -> nx_int |
| 47 | func nx_classical_register_basics(ch: *K2Chain, a: *Term, b: *Term) -> nx_int |