Enduring Strengths of Knowledge-Based Methods in the Era of Machine Learning and Large Language Models: A Task-and-Architecture Perspective

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Large language models have shifted AI toward statistical learning, but knowledge-based methods remain essential for tasks governed by combinatorial structure, declarative correctness, strong domain priors, and auditable reasoning. This paper treats the issue as one of task–architecture fit rather than paradigm competition. It surveys evidence across twelve problem classes, from satisfiability, constraint solving, planning, and formal mathematics to formal argumentation, answer set programming, knowledge graphs, and interpretable rule- and concept-based models, reporting concrete benchmark results instead of broad claims of superiority. From this evidence, the paper proposes nine task characteristics that predict when symbolic, neural, or hybrid approaches are most appropriate, connects them to the major symbolic traditions, and reviews integration patterns such as logic regularization, constraint-guided decoding, search–verification loops, graph retrieval, and probabilistic logic programming. Beyond the survey, an original formal analysis derives error propagation bounds for search–verification loops, convergence conditions for logic regularization, complexity results for constraint-guided decoding across constraint families, and a unified cost-accuracy model for hybrid architectures, and states two characteristic failure modes of hybrid systems as formal propositions. The central conclusion is that robust AI systems increasingly depend on principled hybrids that combine neural flexibility with explicit knowledge and verifiable reasoning.