R-Calculus, V: Description Logics

✍ Scribed by Li Wei, Yuefei Sui

Publisher: Springer
Year: 2025
Tongue: English
Leaves: 393
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Preface to the Series
Preface
Contents
1 Introduction
1.1 Many-Valued Logics
1.2 Multisequents
1.3 Deduction Systems
1.4 Reductions
1.5 R-Calculi
1.6 R-Calculus for Quantifier Constructors
1.7 R-Calculus for Undecidable DL
1.8 Notions
References
Part I Decidable DLs
2 R-Calculus for Binary-Valued DL
2.1 Binary-Valued DL
2.2 1/2-Sequents
2.2.1 Deduction System M1/2t
2.2.2 R-Calculus Rt1/2
2.2.3 Deduction System Nt1/2
2.2.4 R-Calculus St1/2
2.3 1/2-Co-Sequents
2.3.1 Deduction System Lt1/2
2.3.2 R-Calculus Qt1/2
2.3.3 Deduction System Kt1/2
2.3.4 R-Calculus Pt1/2
2.4 2/2-Sequents
2.4.1 Deduction System M=2/2
2.4.2 R-Calculus R=2/2
2.4.3 Deduction System N=2/2
2.4.4 R-Calculus S=2/2
2.5 2/2-Co-Sequents
2.5.1 Deduction System L=2/2
2.5.2 R-Calculus Q=2/2
2.5.3 Deduction System K=2/2
2.5.4 R-Calculus P=2/2
2.6 Conclusions
References
3 R-Calculus for Post Three-Valued DL
3.1 Post Three-Valued DL
3.2 1/3-Multisequents
3.2.1 Deduction System M1/3t
3.2.2 R-Calculus R1/3t
3.3 2/3-Multisequents
3.3.1 Deduction System M2/3tm
3.3.2 R-Calculi R2/3tm
3.4 3/3-Multisequents
3.4.1 Deduction System M=3/3
3.4.2 R-Calculus R=3/3
3.5 Conclusions
References
4 R-Calculus for B22-Valued DL
4.1 B22-Valued DL
4.2 1/22-Multisequents
4.2.1 Deduction System Lt1/22
4.2.2 R-Calculus Q1/22t
4.3 2/22-Multisequents
4.3.1 Deduction System L2t
4.3.2 R-Calculus Q2/22t
4.4 3/22-Multisequents
4.4.1 Deduction System L3/22tperp
4.4.2 R-Calculus Qtperp3/22
4.5 4/22-Multisequents
4.5.1 Deduction System L=4/22
4.5.2 R-Calculus Q=4/22
4.6 Conclusions
References
5 R-Calculi for Post L4-Valued DL
5.1 Post L4-Valued Description Logic
5.2 1/4-Multisequents
5.2.1 Deduction System Nt1/4
5.2.2 R-Calculus St1/4
5.3 2/4-Multisequents
5.3.1 Deduction System N2t
5.3.2 R-Calculus S2/4t
5.4 3/4-Multisequents
5.4.1 Deduction System N3/4tperp
5.4.2 R-Calculus Stperp3/4
5.5 4/4-Multisequents
5.5.1 Deduction System N=4/4
5.5.2 R-Calculus S=4/4
5.6 Conclusions
References
Part II Undecidable DLs
6 Introduction
6.1 Undecidable DL
6.2 R-Calculi
6.3 Post L3-Valued DL with Role Constructors
6.4 B22-Valued DL with Role Constructors
6.5 Injury
6.6 Arrangement of This Part
References
7 Role R-Calculus for Binary-Valued DL
7.1 Binary-Valued DL with Role Constructors
7.2 1/2-Multisequents
7.2.1 Deduction System Mt1/2
7.2.2 R-Calculus Rt1/2
7.2.3 Deduction System N1/2t
7.2.4 R-Calculus S1/2t
7.3 1/2-Co-multisequents
7.3.1 Incomplete Deduction System L1/2t
7.3.2 R-Calculus Qt1/2
7.3.3 Incomplete Deduction System K1/2t
7.3.4 R-Calculus Pt1/2
7.4 2/2-Multisequents
7.4.1 Deduction System M=2/2
7.4.2 R-Calculi R2/2=
7.4.3 Deduction System N2/2=
7.4.4 R-Calculi S=2/2
7.5 2/2-Co-multisequents
7.5.1 Incomplete Deduction System L2/2=
7.5.2 R-Calculi Q=2/2
7.5.3 Incomplete Deduction System K=2/2
7.5.4 R-Calculi P2/2=
7.6 Conclusions
References
8 Role R-Calculus for Post Three-Valued DL
8.1 Post Three-Valued DL with Role Constructors
8.2 1/3-Multisequents
8.2.1 Deduction System Nt1/3
8.2.2 R-Calculus St1/3
8.2.3 Incomplete Deduction System Kt1/3
8.2.4 R-Calculus Pt1/3
8.3 2/3-Multisequents
8.3.1 Deduction System N2/3tm
8.3.2 R-Calculus Stm2/3
8.3.3 Incomplete Deduction System K2/3tm
8.3.4 R-Calculus Ptm2/3
8.4 3/3-Multisequents
8.4.1 Deduction System N=3/3
8.4.2 R-Calculus S=3/3
8.4.3 Incomplete Deduction System K=3/3
8.4.4 R-Calculus P=3/3
8.5 Conclusions
References
9 Role R-Calculus for B22-Valued DL
9.1 B22-Valued DL with Role Constructors
9.2 1/22-Multisequents
9.2.1 Deduction System Mt1/22
9.2.2 R-Calculus R1/22t
9.2.3 Incomplete Deduction System L1/22t
9.2.4 R-Calculus Q1/22t
9.3 2/22-Multisequents
9.3.1 Deduction System Mt2/22
9.3.2 R-Calculus R2/22t
9.4 3/22-Multisequents
9.4.1 Deduction System M3/22tperp
9.4.2 R-Calculus Rtperp3/22
9.5 4/22-Multisequents
9.5.1 Deduction System M=4/22
9.5.2 R-Calculus R=4/22
9.5.3 Incomplete Deduction System L=4/22
9.5.4 R-Calculus Q=4/22
9.6 Conclusions
References
10 Role R-Calculus for Post L4-Valued DL
10.1 Post L4-Valued DL
10.2 1/4-Multisequents
10.2.1 Deduction System Mt1/4
10.2.2 R-Calculus R1/4t
10.2.3 Deduction System Nt1/4
10.2.4 R-Calculus S1/4t
10.3 2/4-Multisequents
10.3.1 Deduction System Nt2/4
10.3.2 R-Calculus S2/4t
10.4 3/4-Multisequents
10.4.1 Deduction System N3/4tperp
10.4.2 R-Calculus Stperp3/4
10.5 4/4-Multisequents
10.5.1 Deduction System M=4/4
10.5.2 R-Calculus R=4/4
10.5.3 Deduction System N=4/4
10.5.4 R-Calculus S=4/4
10.6 Conclusions
References
Appendix: Finite Injury Priority Method
References

📜 SIMILAR VOLUMES

R-Calculus, IV: Propositional Logic

📁 R-Calculus, IV: Propositional Logic

✍ Wei Li, Yuefei Sui 📂 Library 📅 2023 🏛 Springer 🌐 English

This fourth volume of the book series combines propositional logic and R-calculus for a new point of view to consider belief revision. It gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming, ⇝-propositional logic, semantic networks,

R-Calculus, IV: Propositional Logic

📁 R-Calculus, IV: Propositional Logic

✍ Wei Li; Yuefei Sui 📂 Library 📅 2023 🏛 Springer Nature 🌐 English

This fourth volume of the book series combines propositional logic and R-calculus for a new point of view to consider belief revision. It gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming, ⇝-propositional logic, semantic networks, and three

R-Calculus, II: Many-Valued Logics

📁 R-Calculus, II: Many-Valued Logics

✍ Wei Li, Yuefei Sui 📂 Library 📅 2022 🏛 Springer 🌐 English

This second volume of the book series shows R-calculus is a combination of one monotonic tableau proof system and one non-monotonic one. The R-calculus is a Gentzen-type deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM po

R-Calculus, II: Many-Valued Logics

📁 R-Calculus, II: Many-Valued Logics

✍ Wei Li; Yuefei Sui 📂 Library 📅 2022 🏛 Springer Nature 🌐 English

This second volume of the book series shows R-calculus is a combination of one monotonic tableau proof system and one non-monotonic one. The R-calculus is a Gentzen-type deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates

R-Calculus, III: Post Three-Valued Logic

📁 R-Calculus, III: Post Three-Valued Logic

✍ Wei Li, Yuefei Sui 📂 Library 📅 2022 🏛 Springer 🌐 English

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/

Calculator Calculus

📁 Calculator Calculus

✍ George McCarty (auth.) 📂 Library 📅 1982 🏛 Springer US 🌐 English

How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a be