R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui

• Autore: Li Wei <1943 June->
• Pubblicazione: Singapore : , : Science Press, , [2022]; ©2022
• Descrizione fisica: 1 online resource (281 pages)
• Disciplina: 515
• Soggetto topico: Calculus; Logic, Symbolic and mathematical; Computer logic; R (Computer program language)
• Persona (resp. second.): SuiYuefei
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface to the Series -- Preface -- Contents -- 1 Introduction -- 1.1 R-Calculus -- 1.2 Many-Valued Logics -- 1.3 Contents in the First Volume -- 1.4 Contents in This Volume -- 1.5 Notations -- References -- 2 R-Calculus for PL -- 2.1 Basic Definitions -- 2.2 Monotonic Tableau Proof Systems -- 2.2.1 Tableau Proof System Tf -- 2.2.2 Tableau Proof System Tt -- 2.3 Nonmonotonic Tableau Proof Systems -- 2.3.1 Tableau Proof System St -- 2.3.2 Tableau Proof System Sf -- 2.4 R-Calculi -- 2.4.1 R-Calculus Rt -- 2.4.2 R-Calculus Rf -- 2.5 Projecting R-Calculi to Tableau Proof Systems -- 2.6 Notes -- References -- 3 R-Calculus for Description Logic -- 3.1 Basic Definitions -- 3.2 Monotonic Tableau Proof Systems -- 3.2.1 Tableau Proof System Tt -- 3.2.2 Tableau Proof System Tf -- 3.3 Nonmonotonic Tableau Proof Systems -- 3.3.1 Tableau Proof System St -- 3.3.2 Tableau Proof System Sf -- 3.4 R-Calculi -- 3.4.1 R-Calculus Rt -- 3.4.2 R-Calculus Rf -- 3.5 Projecting R-Calculi to Tableau Proof Systems -- References -- 4 R-Calculus for L3-Valued PL -- 4.1 Basic Definitions -- 4.2 Monotonic Tableau Proof Systems -- 4.2.1 Tableau Proof System Tt -- 4.2.2 Tableau Proof System Tm -- 4.2.3 Tableau Proof System Tf -- 4.3 Nonmonotonic Tableau Proof Systems -- 4.3.1 Tableau Proof System St -- 4.3.2 Tableau Proof System Sm -- 4.3.3 Tableau Proof System Sf -- 4.4 R-Calculi -- 4.4.1 R-Calculus Rt -- 4.4.2 R-Calculus Rm -- 4.4.3 R-Calculus Rf -- 4.5 Satisfiability and Unsatisfiability -- 4.5.1 t-Satisfiability and t-Unsatisfiability -- 4.5.2 m-Satisfiability and m-Unsatisfiability -- 4.5.3 f-Satisfiability and f-Unsatisfiability -- 4.6 Projecting R-Calculi to Tableau Proof Systems -- 4.7 Notes -- References -- 5 R-Calculus for L3-Valued PL, II -- 5.1 Monotonic Tableau Proof Systems -- 5.1.1 Tableau Proof System Tt -- 5.1.2 Tableau Proof System Tm. ; 5.1.3 Tableau Proof System Tf -- 5.2 Nonmonotonic Tableau Proof Systems -- 5.2.1 Tableau Proof System St -- 5.2.2 Tableau Proof System Sm -- 5.2.3 Tableau Proof System Sf -- 5.3 R-Calculi -- 5.3.1 R-Calculus Rt -- 5.3.2 R-Calculus Rm -- 5.3.3 R-Calculus Rf -- 5.4 Validity and Invalidity -- 5.4.1 t-Invalidity and t-Validity -- 5.4.2 m-Invalidity and m-Validity -- 5.4.3 f-Invalidity and f-Validity -- 5.5 Projecting R-Calculi to Tableau Proof Systems -- References -- 6 R-Calculus for B22-Valued PL -- 6.1 Basic Definitions -- 6.2 Monotonic Tableau Proof Systems -- 6.2.1 Tableau Proof System Tt -- 6.2.2 Tableau Proof System T -- 6.2.3 Tableau Proof System Tperp -- 6.2.4 Tableau Proof System Tf -- 6.3 Nonmonotonic Tableau Proof Systems -- 6.3.1 Tableau Proof System St -- 6.3.2 Tableau Proof System S -- 6.3.3 Tableau Proof System Sperp -- 6.3.4 Tableau Proof System Sf -- 6.4 R-Calculi -- 6.4.1 R-Calculus Rt -- 6.4.2 R-Calculus R -- 6.4.3 R-Calculus Rperp -- 6.4.4 R-Calculus Rf -- 6.5 Projecting R-Calculi to Tableau Proof Systems -- 6.6 Notes -- References -- 7 R-Calculus for B22-Valued PL,II -- 7.1 Monotonic Tableau Proof Systems Tast1ast2 -- 7.1.1 Tableau Proof System Tt -- 7.1.2 Tableau Proof System Ttperp -- 7.2 Tableau Proof Systems Tast1ast2 -- 7.2.1 Tableau Proof System Tt -- 7.2.2 Tableau Proof System Ttperp -- 7.3 Nonmonotonic Tableau Proof Systems -- 7.3.1 Tableau Proof System St -- 7.3.2 Tableau Proof System Stperp -- 7.3.3 Tableau Proof System St -- 7.3.4 Tableau Proof System Stperp -- 7.4 R-Calculi -- 7.4.1 R-Calculus Rt -- 7.4.2 R-Calculus Rtperp -- 7.4.3 R-Calculus Rf -- 7.4.4 R-Calculus Rfperp -- 7.5 Projecting R-Calculi to Tableau Proof Systems -- 7.6 Notes -- References -- 8 Co-R-Calculus for PL -- 8.1 Co-R-calculi in Propositional Logic -- 8.1.1 Co-R-Calculus Ut -- 8.1.2 Co-R-Calculus Uf -- 8.2 Co-R-Calculi in L3-Valued PL. ; 8.2.1 Co-R-Calculus Ut -- 8.2.2 Co-R-Calculus Um -- 8.2.3 Co-R-Calculus Uf -- 8.3 Co-R-Calculi in B22-Valued Propositional Logic -- 8.3.1 Co-R-Calculus Ut -- 8.4 Notes -- References -- 9 Multisequents and Hypersequents -- 9.1 Tableau Proof Systems -- 9.1.1 Tableau-Typed Proof System Tt -- 9.1.2 Tableau Proof System Tt -- 9.2 Sequents in L3-Valued Propositional Logic -- 9.2.1 Gentzen Deduction System for ΔΣ -- 9.2.2 Gentzen Deduction System for ΘΞ -- 9.2.3 Gentzen Deduction System for ΓΠ -- 9.3 Multisequents in L3-Valued PL -- 9.3.1 Multisequents -- 9.3.2 Co-Multisequents -- 9.4 Hypersequents in L3-Valued PL -- 9.5 Notes -- References -- 10 Product of Two R-Calculi -- 10.1 Tableau Proof Systems in Modalized PL -- 10.1.1 Monotonic Tableau Proof Systems -- 10.1.2 Nonmonotonic Tableau Proof Systems -- 10.2 Product of B2-Valued PLs -- 10.2.1 Tableau Proof System P4t -- 10.2.2 Tableau Proof System P4t -- 10.2.3 Tableau Proof System Qt -- 10.3 Product of Two R-Calculi -- 10.3.1 R-Calculi Rt2 and Rf2 -- 10.3.2 R-Calculus U4t -- 10.4 Notes -- References -- 11 Sum of Two R-Calculi -- 11.1 The Sum with One Common Element -- 11.1.1 B2[f,m]oplusB2[m,t] -- 11.1.2 Operators on Tableau Proof Systems -- 11.1.3 Sum of Tableau Proof Systems -- 11.1.4 R-Calculi -- 11.1.5 R-Calculi in PL -- 11.1.6 R-Calculi in L3-Valued PL -- 11.2 The Sum Without Common Elements -- 11.2.1 L4-Valued PL -- 11.2.2 Equivalences -- 11.2.3 Tableau Proof System Tt4 -- 11.2.4 Tableau Proof System T4 -- 11.2.5 Tableau Proof System Tperp4 -- 11.2.6 Tableau Proof System Tf4 -- 11.2.7 Sum of Tableau Proof Systems: Tt4=sim2(Tt2)oplusTt2 -- 11.2.8 Sum of Tableau Proof Systems: Tt4=Tperp2oplusTt2 -- 11.2.9 Sum of Tableau Proof Systems: St4=Sperp2oplusSt2 -- 11.2.10 Sum of R-Calculi: Rt4equivRperp2oplusRt2 -- 11.3 Notes -- References.
• Titolo autorizzato: R-calculus
• ISBN: 981-16-9293-9; 981-16-9294-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910743342703321
• Lo trovi qui: Univ. Federico II
• Serie: Perspectives in Formal Induction, Revision and Evolution