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This LNCS conference volume constitutes the proceedings of the 13th International Symposium, FoIKS 2024, in Sheffield, UK, in April 2024. The 18 full papers together with 3 short papers included in this volume were carefully reviewed and selected from 42 submissions. The Symposium focuses on fundamental aspect of information and knowledge systems, including submissions that apply ideas, theories, or methods from specific disciplines to information and knowledge systems. Examples of such disciplines are discrete mathematics, logic and algebra, model theory, databases, information theory, complexity theory, algorithmics and computation, statistics, and optimization.