Gayane Humanitarian Logic (GHL): A Set-Theoretic and Syllogistic Extension of Gayane Quaternary Logic (GL4) - Mathematical Apparatus, Ontology, and Composition Tables

Gayane Humanitarian Logic (GHL) is a set-theoretic and syllogistic extension of Gayane Quaternary Logic (GL4). GL4 is a two-dimensional four-valued logic built on Verity (True/False) and Inevitability (Inevitable/Avoidable) axes, yielding 4 elementary values B,C,D,E and 16 composite values. GHL interprets them as quantifiers: B=none (empty), E=all (homogeneous), M=at least one, H=at most part, P=only part (mixed), I=totality. This release v0.0.5 presents:- Ontology of one property: 4 mutually exclusive natural states- Ontology of two properties: 8 atomic relations and 256 composite relations formed by strict disjunction- Full composition tables via minimal epistemic set {M!x, M!~x, B!x, B!~x}- Axiomatic hierarchy: Van, Sevan, Goris, Ani, Artashat, Karin- Syntax: affirmative ! vs negative # , three negations ~ ¬ ≠ , 256 unary operators Full theoretical apparatus and abstracts in 5 languages (EN, DE, FR, HY, RU) are inside the file. Base work: GL4 DOI 10.5281/zenodo.21641412 [CC BY 4.0]This work: GHL v0.0.5 DOI 10.5281/zenodo.21828122 [CC BY-NC 4.0] Theoretical publication only. Concrete binary/quaternary encodings, bit-level and hardware optimizations, and MartML implementation are proprietary and not included. Commercial license: oganmart1980@gmail.comAuthor: Martirosyan Hovhannes, Armavir, Armenia https://www.linkedin.com/in/hovhannes-martirosyan-2637823b5/ https://www.facebook.com/martirosyan.ogannes oganmart1980@gmail.com