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This book series consists of two parts, decidable description logics and undecidable description logics. It gives the R-calculi for description logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.

This book illustrates how to use description logic-based formalisms to their full potential in the creation, indexing, and reuse of multimedia semantics. To do so, it introduces researchers to multimedia semantics by providing an in-depth review of state-of-the-art standards, technologies, ontologies, and software tools. It draws attention to the importance of formal grounding in the knowledge representation of multimedia objects, the potential of multimedia reasoning in intelligent multimedia applications, and presents both theoretical discussions and best practices in multimedia ontology engineering. Readers already familiar with mathematical logic, Internet, and multimedia fundamentals will learn to develop formally grounded multimedia ontologies, and map concept definitions to high-level descriptors. The core reasoning tasks, reasoning algorithms, and industry-leading reasoners are presented, while scene interpretation via reasoning is also demonstrated.Overall, this book offers readers an essential introduction to the formal grounding of web ontologies, as well as a comprehensive collection and review of description logics (DLs) from the perspectives of expressivity and reasoning complexity. It covers best practices for developing multimedia ontologies with formal grounding to guarantee decidability and obtain the desired level of expressivity while maximizing the reasoning potential. The capabilities of such multimedia ontologies are demonstrated by DL implementations with an emphasis on multimedia reasoning applications.

Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge.A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.