作者：李未，眭跃飞
页数：212
出版社：科学出版社
出版日期：2023
ISBN：9787030764102
电子书格式：pdf/epub/txt
内容简介
R-演算是非单调的Gentzen型演绎系统，是一种具体的信念修正算子，被证明满足AGM假设和DP假设。本书是为了扩展R演算（i）从一阶逻辑到命题逻辑，描述逻辑，模态逻辑和逻辑编程；（ii）从最小变化语义到子集最小变化，伪子公式最小变化和基于演绎的最小变化（最后两个最小变化是新定义的）；并针对这些极小值证明合理性和完整性定理。这些逻辑的变化。为了使R-演算可计算，我们在递归理论中给出了使用有限伤害优先级方法的近似R-演算。此外，R演算的两个应用被赋予了默认理论和语义继承网络。
目录
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-subfor
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-subfor
