Gayane Logical Quartet: Totality and Partiality as Complete Ontology

Abstract

Abstract: A fourfold structure observed in language, thought and nature is introduced: All / This part / Other part / Nothing. It consists of two super-categories — Totality and Partiality — read in GL4 as Inevitable / Avoidable and in GHL as All+None / Part. Two super-categories:- TOTALITY = INEVITABLE: E = IT Inevitable True (All, Always, Everywhere), B = IF Inevitable False (None, Never, Nowhere)- PARTIALITY = AVOIDABLE: D = PT Avoidable True (This part), C = PF Avoidable False (Other part)Core law: P!x == P!~x — part exists only through other part. Formula: {B} ⊻ E!x ⊻ (M!x ∧ M!~x) This is the philosophical foundation for:GL4 — DOI 10.5281/zenodo.21641412GHL — DOI 10.5281/zenodo.21828122 Full paper in PDF. HD tables in PNG.Author: Martirosyan Hovhannes, 2026. CC BY 4.0