R-Calculus, III: Post Three-Valued Logic

This third volume of the book series shows R-calculus is a Gentzen-typed deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given.

This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.

Discusses the algebraical and logical properties of tableau proof systems and R-calculi in many-valued logics Gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming etc. Inspires theoretic computer scientists by showing how R-calculus is developed into a series of complicated theories

Auteur
Wei Li, is a Professor in the School of Computer Science and Engineering, Beihang University, Beijing, China and is a member of the Chinese Academy of Sciences. Prof. Li is mostly engaged in the applied research of Computer Software and Theory, and the Internet, including programming languages, software development, artificial intelligence, and integrated circuit design.

Yuefei Sui, is a Professor in the Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China. His main interests include knowledge representation, applied logic and the theory of computability.

Résumé

"The book is well-structured and provides a detailed exploration of the subject matter. It appears to be a valuable resource for those interested in the field of logic and belief revision." (Albert Hoogewijs, zbMATH 1525.03001, 2024)

Contenu

Introduction.- Many-Placed Sequents.- Modalized Three-Valued Logics.- Post three-valued logic.- R-Calculi for Post Three-valued logic.- Post Three-valued description logic.- R-calculi for Post three-valued description logic.- R-calculi for corner multisequents.- General multisequents.- R-calculi for general multisequents.