UniLog: A Unified Logic Framework for Constraint Representation and Handling in Intelligent Systems

This paper presents UniLog, a unified logic framework designed to integrate the expressive power and reasoning capabilities of diverse logical systems into a single coherent formalism. UniLog is specifically developed to serve as the constraint representation language for the Constrained Object Hierarchies (COH) and Constrained Zone-Object Architecture (CZOA) frameworks, enabling the specification of identity constraints, trigger constraints, goal constraints, and access constraints in a unified manner. The core novelty of UniLog lies not in any single logic but in its architecture: a modular, fibred system that combines a core modal‑temporal substructure with conservatively extended modules for probabilistic, non‑monotonic, epistemic, and domain‑specific reasoning. We provide formal syntax, semantics, and inference rules for UniLog, demonstrate its embedding of major logic families, and illustrate its application to complex organizational intelligent information systems. In addition, we establish key meta‑theoretic properties: conservativity of modular extensions (Theorem 3), soundness of the inference system, decidability of useful fragments, and soundness and relative completeness of a translation from a bounded fragment of UniLog to SMT‑LIB. These results provide a rigorous foundation for using UniLog in formal verification and for integrating it with automated theorem provers.