Truth4 Logic

Truth4 Logic (I.D21) is the τ-internal four-valued logic — extending classical bivalence (true/false) with the structural truth values reflecting the kernel's bipolar polarity. With 46 incoming edges, it is the second most-referenced kernel definition (after Prime Polarity T06) and the substrate for the framework's logical reasoning across τ-categorical content.

Categorical invariant. A four-element distributive lattice T4 := {⊥, +, −, ⊤} with operations compatible with K3 composition and Prime Polarity (T06).

Primary registry anchor: I.D21

Supporting items: I.T05, I.D20

1. I.K0 — Universe Postulate
2. I.T05 — Prime Polarity — bipolar {+, −} structure
3. I.D21 — Truth4 Logic — extend bipolar to four values {⊥, +, −, ⊤}

Lean modules referenced: TauLib.BookI.Logic.Truth4

Status: Formalized

Module: TauLib.BookI.Logic.Truth4

Lean kind: structure

Lean symbol: Tau.BookI.Logic.Truth4