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R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui
R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui
Autore Li Wei <1943 June->
Pubbl/distr/stampa Singapore : , : Science Press, , [2022]
Descrizione fisica 1 online resource (281 pages)
Disciplina 515
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Calculus
Logic, Symbolic and mathematical
Computer logic
R (Computer program language)
ISBN 981-16-9294-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNISA-996472064903316
Li Wei <1943 June->  
Singapore : , : Science Press, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui
R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui
Autore Li Wei <1943 June->
Pubbl/distr/stampa Singapore : , : Science Press, , [2022]
Descrizione fisica 1 online resource (281 pages)
Disciplina 515
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Calculus
Logic, Symbolic and mathematical
Computer logic
R (Computer program language)
ISBN 981-16-9293-9
981-16-9294-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNISA-996549469503316
Li Wei <1943 June->  
Singapore : , : Science Press, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui
R-calculus . II : Many-valued logics / / Wei Li, Yuefei Sui
Autore Li Wei <1943 June->
Pubbl/distr/stampa Singapore : , : Science Press, , [2022]
Descrizione fisica 1 online resource (281 pages)
Disciplina 515
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Calculus
Logic, Symbolic and mathematical
Computer logic
R (Computer program language)
ISBN 981-16-9293-9
981-16-9294-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNINA-9910743342703321
Li Wei <1943 June->  
Singapore : , : Science Press, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
R-CALCULUS : a logic of belief revision / / Wei Li, Yuefei Sui
R-CALCULUS : a logic of belief revision / / Wei Li, Yuefei Sui
Autore Li Wei
Pubbl/distr/stampa Singapore : , : Springer, , [2021]
Descrizione fisica 1 online resource (210 pages)
Disciplina 515
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Calculus
Software
Mathematical Concepts
R (Computer program language)
ISBN 981-16-2944-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNISA-996464408403316
Li Wei  
Singapore : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
R-CALCULUS : a logic of belief revision / / Wei Li, Yuefei Sui
R-CALCULUS : a logic of belief revision / / Wei Li, Yuefei Sui
Autore Li Wei
Pubbl/distr/stampa Singapore : , : Springer, , [2021]
Descrizione fisica 1 online resource (210 pages)
Disciplina 515
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Calculus
Software
Mathematical Concepts
R (Computer program language)
ISBN 981-16-2944-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNINA-9910508455003321
Li Wei  
Singapore : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
R-calculus, III : post three-valued logic / / Wei Li, Yuefei Sui
R-calculus, III : post three-valued logic / / Wei Li, Yuefei Sui
Autore Li Wei
Pubbl/distr/stampa Singapore : , : Springer, , [2022]
Descrizione fisica 1 online resource (284 pages)
Disciplina 515
Collana Perspectives in formal induction, revision and evolution
Soggetto topico Calculus
Computer logic
Proof theory
ISBN 981-19-4270-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNISA-996499855203316
Li Wei  
Singapore : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
R-calculus, III : post three-valued logic / / Wei Li, Yuefei Sui
R-calculus, III : post three-valued logic / / Wei Li, Yuefei Sui
Autore Li Wei
Pubbl/distr/stampa Singapore : , : Springer, , [2022]
Descrizione fisica 1 online resource (284 pages)
Disciplina 515
Collana Perspectives in formal induction, revision and evolution
Soggetto topico Calculus
Computer logic
Proof theory
ISBN 981-19-4270-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
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.
Record Nr. UNINA-9910631080703321
Li Wei  
Singapore : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
R-Calculus, IV : propositional logic / / Wei Li and Yuefei Sui
R-Calculus, IV : propositional logic / / Wei Li and Yuefei Sui
Autore Li Wei
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Singapore : , : Springer, , [2023]
Descrizione fisica 1 online resource (264 pages)
Disciplina 810
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Propositional calculus
ISBN 9789811986338
9789811986321
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- R-calculus for simplified propositional logics -- R-calculi for tableau/Gentzen deduction systems -- R-calculi RQ1Q2/RQ1Q2 -- R-calculi RQ1iQ2j/RQ1iQ2j -- R-Calculi: RY1Q1iY2Q2j/RY1Q1iY2Q2j -- R-calculi for supersequents -- R-calculi for propositional logic.
Record Nr. UNINA-9910683352003321
Li Wei  
Singapore : , : Springer, , [2023]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
R-Calculus, IV : propositional logic / / Wei Li and Yuefei Sui
R-Calculus, IV : propositional logic / / Wei Li and Yuefei Sui
Autore Li Wei
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Singapore : , : Springer, , [2023]
Descrizione fisica 1 online resource (264 pages)
Disciplina 810
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Propositional calculus
ISBN 9789811986338
9789811986321
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- R-calculus for simplified propositional logics -- R-calculi for tableau/Gentzen deduction systems -- R-calculi RQ1Q2/RQ1Q2 -- R-calculi RQ1iQ2j/RQ1iQ2j -- R-Calculi: RY1Q1iY2Q2j/RY1Q1iY2Q2j -- R-calculi for supersequents -- R-calculi for propositional logic.
Record Nr. UNISA-996546834003316
Li Wei  
Singapore : , : Springer, , [2023]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
R-Calculus, V: Description Logics / / by Wei Li, Yuefei Sui
R-Calculus, V: Description Logics / / by Wei Li, Yuefei Sui
Autore Li Wei <1625-1684, >
Edizione [1st ed. 2024.]
Pubbl/distr/stampa Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024
Descrizione fisica 1 online resource (XIII, 384 p. 4 illus., 1 illus. in color.)
Disciplina 515
Collana Perspectives in Formal Induction, Revision and Evolution
Soggetto topico Machine theory
Logic, Symbolic and mathematical
Logic programming
Mathematical models
Computer science - Mathematics
Big data
Formal Languages and Automata Theory
Mathematical Logic and Foundations
Logic in AI
Mathematical Modeling and Industrial Mathematics
Mathematics of Computing
Big Data
ISBN 981-9964-60-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction -- Decidable DLs 30 -- R-calculus for binary-valued description logic -- R-calculi for Post three-valued DL -- R-calculi for B22-valued DL -- R-calculi for Post L4 -valued DL -- Undecidable DLs -- Introduction -- Role R-calculus for binary-valued DL -- Role R-calculus for Post three-valued DL -- Role R-calculus for B22 -valued DL -- Role R-calculus for Post L4-valued DL -- A Finite injury priority method.
Record Nr. UNINA-9910799238103321
Li Wei <1625-1684, >  
Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui