Record Nr.

UNINA9910631080703321

Autore

Li Wei

Titolo

R-calculus, III : post three-valued logic / / Wei Li, Yuefei Sui

Pubbl/distr/stampa


Singapore : , : Springer, , [2022]
©2022

ISBN

981-19-4270-6

Descrizione fisica

1 online resource (284 pages)

Collana

Perspectives in formal induction, revision and evolution

Disciplina

515

Soggetti

Calculus

Computer logic

Proof theory

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 Three-Valued Logics -- 1.2 Deduction Systems -- 1.3 R-Calculi -- 1.4 More -- 1.5 Basic Definitions -- 1.5.1 Post Three-Valued Logic -- 1.5.2 Post Three-Valued Description Logic -- 1.5.3 Remarks -- 1.6 Types of Deduction Rules -- 1.7 Notations -- References -- 2 Many-Placed Sequents -- 2.1 Zach's Theorem -- 2.2 Analysis of Zach's Theorem -- 2.3 Tableau Proof Systems -- 2.3.1 Tableau Proof System Tt -- 2.3.2 Tableau Proof System Tm -- 2.3.3 Tableau Proof System Tf -- 2.4 Incompleteness of Deduction System T'' -- References -- 3 Modalized Three-Valued Logics -- 3.1 Bochvar Three-Valued Logic -- 3.1.1 Basic Definitions -- 3.1.2 Multisequent Deduction System Mb -- 3.2 Kleene Three-Valued Logic -- 3.2.1 Basic Definitions -- 3.2.2 Gentzen Deduction System Gk -- 3.3 Łukasiewicz's Three-Valued Logic -- 3.3.1 Basic Definitions -- 3.3.2 Tableau Proof System Tl -- References -- 4 Post Three-Valued Logic -- 4.1 Theories -- 4.1.1 Tableau Proof System Tt -- 4.1.2 Tableau Proof System Tm -- 4.1.3 Tableau Proof System Tf -- 4.1.4 Transformations -- 4.1.5 Tableau Proof System Tt -- 4.1.6 Tableau Proof System Tm -- 4.1.7 Tableau Proof System Tf -- 4.2 Sequents -- 4.2.1 Gentzen Deduction System Gt -- 4.2.2 Gentzen Deduction System Gm -- 4.2.3 Gentzen Deduction System Gf -- 4.2.4 Gentzen Deduction System Gt -- 4.2.5 Gentzen

Deduction System Gm -- 4.2.6 Gentzen Deduction System Gf -- 4.3 Multisequents -- 4.3.1 Gentzen Deduction System M= -- 4.3.2 Simplified Ms= -- 4.3.3 Gentzen Deduction System M= -- 4.3.4 Simplified Ms= -- 4.3.5 Cut Elimination Theorem -- References -- 5 R-Calculi for Post Three-Valued Logic -- 5.1 R-Calculus for Theories -- 5.1.1 R-Calculus Rt -- 5.1.2 R-Calculus Rt -- 5.2 R-Calculi East for Sequents -- 5.2.1 R-Calculus Et -- 5.2.2 R-Calculus Em -- 5.2.3 Basic Theorems.

5.3 R-Calculi for Multisequents -- 5.3.1 R-Calculus K= -- 5.3.2 Simplified K=s -- 5.3.3 R-Calculus K= -- 5.3.4 R-Calculus K=s -- References -- 6 Post Three-Valued Description Logic -- 6.1 Theories -- 6.1.1 Tableau Proof System St -- 6.1.2 Tableau Proof System St -- 6.2 Sequents -- 6.2.1 Gentzen Deduction System Ft -- 6.2.2 Gentzen Deduction System Ft -- 6.3 Multisequents -- 6.3.1 Gentzen Deduction System L= -- 6.3.2 Simplified Ls= -- 6.3.3 Gentzen Deduction System L= -- 6.3.4 Simplified Ls= -- References -- 7 R-Calculi for Post Three-Valued Description Logic -- 7.1 R-Calculus for Theories -- 7.1.1 R-Calculus Qt -- 7.1.2 R-Calculus Qt -- 7.2 R-Calculi for Sequents -- 7.2.1 R-Calculus Dt -- 7.2.2 R-Calculus Dm -- 7.3 R-Calculi for Multisequents -- 7.3.1 R-Calculus J= -- 7.3.2 Simplified J=s -- 7.3.3 Simplified J= -- References -- 8 R-Calculi for Corner Multisequents -- 8.1 Corner Multisequents MQQQ= -- 8.1.1 Axioms -- 8.1.2 Deduction Rules -- 8.1.3 Deduction Systems -- 8.2 Corner Multisequents MQQQ= -- 8.2.1 Axioms -- 8.2.2 Deduction Rules -- 8.2.3 Deduction Systems -- 8.3 R-Calculi KQQQ=/KQQQ= -- 8.3.1 Axioms -- 8.3.2 Deduction Rules -- 8.3.3 Deduction Systems -- 8.4 R-Calculi JQQQ=/JQQQ= -- 8.4.1 Axioms -- 8.4.2 Deduction Rules -- 8.4.3 Deduction Systems -- References -- 9 General Multisequents -- 9.1 General Multisequents -- 9.2 Axioms -- 9.2.1 Axioms for M=/M= -- 9.2.2 Axioms for L=/L=-Validity -- 9.3 Deduction Rules -- 9.4 Deduction Systems -- References -- 10 R-Calculi for General Multisequents -- 10.1 R-Calculi K=Q1Q2Q3/K=Q1Q2Q3/J=Q1Q2Q3/J=Q1Q2Q3 -- 10.2 Axioms -- 10.2.1 Axioms for K=Q1Q2Q3/K=Q1Q2Q3 -- 10.2.2 Axioms for J=Q1Q2Q3/J=Q1Q2Q3 -- 10.3 Deduction Rules -- 10.3.1 R+= -- 10.3.2 R+= -- 10.3.3 R-= -- 10.3.4 R-= -- 10.4 Deduction Systems -- References.