axiom vs ontology

axiom

noun
  • A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context). 

  • A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved. 

  • An established principle in some artistic practice or science that is universally received. 

ontology

noun
  • In a subject view, or a world view, the set of conceptual or material things or classes of things that are recognised as existing, or are assumed to exist in context, and their interrelations; in a body of theory, the ontology comprises the domain of discourse, the things that are defined as existing, together with whatever emerges from their mutual implications. 

  • A logical system involving theory of classes, developed by Stanislaw Lesniewski (1886-1939). 

  • A structure of concepts or entities within a domain, organized by relationships; a system model. 

  • The theory of a particular philosopher or school of thought concerning the fundamental types of entity in the universe. 

  • The branch of metaphysics that addresses the nature or essential characteristics of being and of things that exist; the study of being qua being. 

How often have the words axiom and ontology occurred in a corpus of books? (source: Google Ngram Viewer )