Automated Deduction in Propositional Logic for Knowledge Base Validation: Ensuring Consistency and Completeness

Abstract

Automated deduction in propositional logic has gained increasing relevance in contemporary knowledge-based systems, especially with the ever-growing need to maintain extensive databases that capture a wide range of real-world information. This paper explores rigorous methodologies for ensuring consistency and completeness within knowledge bases, focusing on the application of automated deduction techniques tailored for propositional logic. We address the systematic detection and resolution of contradictions, offering a framework that integrates proof-based mechanisms and model-checking methods to verify the logical soundness of curated data. The central motivation behind this work is to enable practitioners to construct, expand, and revise large-scale knowledge repositories with confidence in their logical correctness and reliability. By examining diverse logical theorems and strategies—ranging from resolution-based procedures to advanced heuristic-driven solvers—we demonstrate how to effectively identify inconsistencies in complex propositional structures. Additionally, we highlight how linear algebraic formulations can support certain inference processes, thereby improving both interpretability and computational efficiency. The paper offers a generalizable approach that can be adapted to various domains, including semantic web technologies, intelligent agent architectures, and real-time decision support systems. Ultimately, the integration of automated deduction in propositional logic ensures a robust foundation for knowledge base validation, preventing critical errors that might compromise the overall integrity of the systems that rely upon them.