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1. |
Record Nr. |
UNISA996499855203316 |
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Autore |
Li Wei |
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Titolo |
R-calculus, III : post three-valued logic / / Wei Li, Yuefei Sui |
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Pubbl/distr/stampa |
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Singapore : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Descrizione fisica |
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1 online resource (284 pages) |
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Collana |
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Perspectives in formal induction, revision and evolution |
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Disciplina |
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Soggetti |
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Calculus |
Computer logic |
Proof theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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 |
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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. |
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2. |
Record Nr. |
UNINA9910807419303321 |
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Autore |
Yixuan -867 |
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Titolo |
The record of Linji : a new translation of the Linjilu in the light of ten Japanese Zen commentaries / / Jeffrey L. Broughton ; with Elise Yoko Watanabe |
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Pubbl/distr/stampa |
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Oxford : , : Oxford University Press, , [2013] |
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©2013 |
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ISBN |
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Descrizione fisica |
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1 online resource (272 p.) |
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Disciplina |
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Soggetti |
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Linji (Sect) |
Zen Buddhism |
Zen literature - Japan |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references (pages 289-292) and index. |
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Sommario/riassunto |
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The Linjilu (Record of Linji or LJL) is one of the foundational texts of Chan/Zen Buddhist literature, and an accomplished work of baihua (vernacular) literature. Its indelibly memorable title character, the Master Linji-infamous for the shout, the whack of the rattan stick, and the declaration that sutras are toilet paper-is himself an embodiment of the very teachings he propounds to his students: he is a "true person," free of dithering; heexhibits the non-verbal, unconstrained spontaneity of the buddha-nature; he is always active, never passive; and he is aware that nothing is lacking at all, at any time, in his round of daily activities. This bracing new translation transmits the LJL's living expression of Zen's "personal realization of the meaning beyond words," asinterpreted by ten commentaries produced by Japanese Zen monks, over a span of over four centuries, ranging from the late 1300s, when Five-Mountains Zen flourished in Kyoto and Kamakura, through the early 1700s, an age of thriving interest in the LJL. These Zen commentaries form a body of vital, in-house interpretive literature never before given full credit or center stage in previous translations of the LJL. Here, their insights are fully incorporated into the |
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translationitself, allowing the reader unimpeded access throughout, with more extensive excerpts available in the notes. Also provided is a translation of the earliest extant material on Linji, including a neglected transmission-record entry relating to his associate Puhua, which indicate that the LJL is a fully-fledged workof literature that has undergone editorial changes over time to become the compelling work we know today. |
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