1 Introduction 1.1 Belief Revision 1.2 R-Calculus 1.3 Extending R-Calculus 1.4 Approximate R-Calculus 1.5 Applications of R-Calculus References 2 Preliminaries 2.1 Propositional Logic 2.1.1 Syntax and Semantics 2.1.2 Gentzen Deduction System 2.1.3 Soundness and Completeness Theorem 2.2 First-Order Logic 2.2.1 Syntax and Semantics 2.2.2 Gentzen Deduction System 2.2.3 Soundness and Completeness Theorem 2.3 Description Logic 2.3.1 Syntax and Semantics 2.3.2 Gentzen Deduction System 2.3.3 Completeness Theorem References 3 R-Calculi for Propositional Logic 3.1 Minimal Changes 3.1.1 Subset-Minimal Change 3.1.2 Pseudo-Subformulas-Minimal Change 3.1.3 Deduction-Based Minimal Change 3.2 R-Calculus for Minimal Change 3.2.1 R-Calculus S for a Formula 3.2.2 R-Calculus S for a Theory 3.2.3 AGM Postulates A for Minimal Change 3.3 R-Calculus for 5-Minimal Change 3.3.1 R-Calculus T for a Formula 3.3.2 R-Calculus T for a Theory 3.3.3 AGM Postulates A for Minimal Change 3.4 R-Calculus for S Minimal Change 3.4.1 R-Calculus U for a Formula 3.4.2 R-Calculus U for a Theory References 4 R-Calculi for Description Logics 4.1 R-Calculus for Minimal Change 4.1.1 R-Calculus SDL for a Statement 4.1.2 R-Calculus SDL for a Set of Statements 4.2 R-Calculus for Minimal Change 4.2.1 Pseudo-Subconcept-Minimal Change 4.2.2 R-Calculus TDL for a Statement 4.2.3 R-Calculus TDL for a Set of Statements 4.3 Discussion on R-Calculus fo Minimal Change References 5 R-Calculi for Modal Logic 5.1 Propositional Modal Logic
5.2 R-Calculus SM for Minimal Change 5.3 R-Calculus TM for Minimal Change 5.4 R-Modal Logic 5.4.1 A Logical Language of R-Modal Logic 5.4.2 R-Modal Logic References 6 R-Calculi for Logic Programming 6.1 Logic Programming 6.1.1 Gentzen Deduction Systems 6.1.2 Dual Gentzen Deduction System 6.1.3 Minimal Change 6.2 R-Calculus SLP for C-Minimal Change 6.3 R-Calculus TLP for Minimal Change References 7 R-Calculi for First-Order Logic 7.1 R-Calculus for Minimal Change 7.1.1 R-Calculus SFOL for a Formula 7.1.2 R-Calculus SFOL for a Theory 7.2 R-Calculus for Minimal Change 7.2.1 R-Calculus T FOL for a Formula 7.2.2 R-Calculus T FOE for a Theory References 8 Nonmonotonicity of R-Calculus 8.1 Nonmonotonic Propositional Logic 8.1.1 Monotonic Gentzen Deduction System G1 8.1.2 Nonmonotonic Gentzen Deduction System Logic G2 8.1.3 Nonmonotonicity of G2 8.2 Involvement of F A in a Nonmonotonic Logic 8.2.1 Default Logic 8.2.2 Circumscription 8.2.3 Autoepistemic Logic 8.2.4 Logic Programming with Negation as Failure 8.3 Correspondence Between R-Calculus and Default Logic 8.3.1 Transformation from R-Calculus to Default Logic 8.3.2 Transformation from Default Logic to R-Calculus References 9 Approximate R-Calculus 9.1 Finite Injury Priority Method 9.1.1 Post's Problem 9.1.2 Construction with Oracle 9.1.3 Finite Injury Priority Method 9.2 Approximate Deduction 9.2.1 Approximate Deduction System for First-Order Logic 9.3 R-Calculus Fapp and Finite Injury Priority Method 9.3.1 Construction with Oracle 9.3.2 Approximate Deduction System F app 9.3.3 Recursive Construction 9.3.4 Approximate R-Calculus F rec 9.4 Default Logic and Priority Method 9.4.1 Construction of an Extension without Injury
9.4.2 Construction of a Strong Extension with Finite Injury Priority Method References 10 An Application to Default Logic 10.1 Default Logic and Subset-Minimal Change 10.1.1 Deduction System SD for a Default 10.1.2 Deduction System SD for a Set of Defaults 10.2 Default Logic and Pseudo-subformula-minimal Change 10.2.1 Deduction System TD for a Default 10.2.2 Deduction System TD for a Set of Defaults 10.3 Default Logic and Deduction-Based Minimal Change 10.3.1 Deduction System UD for a Default 10.3.2 Deduction System UD for a Set of Defaults References 11 An Application to Semantic Networks 11.1 Semantic Networks 11.1.1 Basic Definitions 11.1.2 Deduction System G4 for Semantic Networks 11.1.3 Soundness and Completeness Theorem 11.2 R-Calculus for c-Minimal Change 11.2.1 R-Calculus SSN for a Statement 11.2.2 Soundness and Completeness Theorem 11.2.3 Examples 11.3 R-Calculus for -Minirnal Change 11.3.1 R-Calculus TSN for a Statement 11.3.2 Soundness and Completeness Theorem of TSN References Index
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