R-CALCULUS : a logic of belief revision / / Wei Li, Yuefei Sui

• Record Nr.: UNISA996464408403316
• Autore: Li Wei
• Pubbl/distr/stampa: Singapore : , : Springer, , [2021]; ©2021
• ISBN: 981-16-2944-7
• Descrizione fisica: 1 online resource (210 pages)
• Collana: Perspectives in Formal Induction, Revision and Evolution
• Disciplina: 515
• Soggetti: Calculus; Software; Mathematical Concepts; R (Computer program language)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface to the Series -- Preface -- Contents -- 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 subseteq-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 Asubseteq for subseteq-Minimal Change -- 3.3 R-Calculus for preceq-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 Apreceq for preceq-Minimal Change -- 3.4 R-Calculus for vdashpreceq-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 subseteq-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 preceq-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 for vdashpreceq-Minimal Change -- References -- 5 R-Calculi for Modal Logic -- 5.1 Propositional Modal Logic -- 5.2 R-Calculus SM for subseteq-Minimal Change.; 5.3 R-Calculus TM for preceq-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 subset-Minimal Change -- 6.3 R-Calculus TLP for preceq-Minimal Change -- References -- 7 R-Calculi for First-Order Logic -- 7.1 R-Calculus for subseteq-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 preceq-Minimal Change -- 7.2.1 R-Calculus TFOL for a Formula -- 7.2.2 R-Calculus TFOL for a Theory -- References -- 8 Nonmonotonicity of R-Calculus -- 8.1 Nonmonotonic Propositional Logic -- 8.1.1 Monotonic Gentzen Deduction System G'1 -- 8.1.2 Nonmonotonic Gentzen Deduction System Logic G2 -- 8.1.3 Nonmonotonicity of G2 -- 8.2 Involvement of ΓA 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 Fapp -- 9.3.3 Recursive Construction -- 9.3.4 Approximate R-Calculus Frec -- 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 subseteq-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 preceq-Minimal Change -- 11.3.1 R-Calculus TSN for a Statement -- 11.3.2 Soundness and Completeness Theorem of TSN -- References -- Index.