Ontological Logic

Abstract

I propose Ontological Logic as a foundational component of the broader Empirical-Axiomatic Framework (EAF) for analyzing existence, representation, logical structure, abstraction, and knowledge. The central distinction developed in this work is between an underlying existent or abstract structure and the representation through which it is described. Although propositions, equations, definitions, axioms, postulates, and theorems are indispensable for knowledge and communication, they are not identical to the underlying structural content they represent. I therefore consider logical structure at an ontological level by replacing the foundational focus on truth and falsity with the existence statuses E (exists) and N (does not exist), while retaining the familiar logical operations ¬, ∧, and ∨. Building on this distinction, I develop an existence-based interpretation of logical relations, consistency, admissibility, and configurations of existents, and introduce the concept of an ontological information space to distinguish the broader domain of structural content from the portion currently represented or known by an epistemic agent. I further propose a set-theoretic and symbolic formulation for abstract structures in which foundational representational components such as axioms, assumptions, postulates, definitions, and foundational facts or relations are assigned symbolic identifiers and organized as a generator set. Theorems are then represented as relations among these structural components. This formulation deliberately separates the structural role of definitions from that of theorems, independently of the chronological order in which particular mathematical concepts are introduced. Its principal purpose is symbolic compression: to represent complex abstract structures through a compact system of identifiable components and logical relations without identifying the representation with the underlying structure. The framework is illustrated conceptually through mathematical and physical structures including Euclidean geometry, group theory, linear algebra, real analysis, and classical mechanics. The work establishes a conceptual foundation for this approach while recognizing that its complete axiomatization and rigorous formal mathematical development remain open for further investigation.