Natural deduction : a proof-theoretical study.
Series Acta Universitatis Stockholmiensis. 3Stockholm studies in philosophyEditor: Stockholm [etc.] : Almqvist & Wiksell, 1965Descripción: 113 p. ; 24 cmTema(s): Gentzen, GerhardOtra clasificación: 03FxxI I. NATURAL DEDUCTION OF GENTZEN-TYPE § I. The languages of first order [13] § 2. Inference rules and deductions [16] § 3. Notions concerning deductions [25] § 4. An alternative definition of the deductions [29] II. THE INVERSION PRINCIPLE § i. Properties of the inference rules [32] i § 2. Reduction steps [35] III. NORMAL DEDUCTIONS IN CLASSICAL LOGIC § i| Theorem on normal deductions [39] § 2. The form of normal deductions [41] § 3. Some further corollaries [44] IV. NORMAL DEDUCTIONS IN INTUITIONISTIC LOGIC § i. Theorem on normal deductions [49] § 2. The form of normal deductions [52] § 3. Some further corollaries [54] V. SECOND ORDER LOGIC § 1. Natural deduction for second order logic [63] § 2. Normal deductions in ramified 2nd order logic [68] § 3. The unprovability by finitary methods of the theorem on normal deductions for simple 2nd order logic [71] VI. MODAL LOGIC § 1. Natural deduction for modal logic [74] § 2. Essentially modal formulas [76] § 3. Normal deductions in the S4-systems [78] § 4. Normal deductions in C'S5 [80] VII. SOME OTHER CONCEPTS OF IMPLICATION § i. Relevant implication [81] § 2. Relevant implication extended by minimal and classical logic [83] § 3. Rigorous implication [86] APPENDIX A. THE CALCULI OF SEQUENTS § i. Definition of the calculi of sequents [88] § 2. Connections between the calculi of sequents and the systems of natural deduction [90] § 3. Gentzen’s Hauptsatz [91] APPENDIX B. ON A SET THEORY BY FITCH § i. A demonstrably consistent set theory [94] § 2. The relation of the system F to Fitch’s system [96] APPENDIX C. NOTES ON SOME OTHER VARIANTS OF NATURAL DEDUCTION § i. The origin of natural deduction [98] § 2. Variants of Gentzen-type systems [101] § 3. Rules for existential instantiation [103]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 03 P918 (Browse shelf) | Available | A-3168 |
Akademisk avhandling--Stockholm. Universitet.
Bibliografía: p. [106]-109.
I I. NATURAL DEDUCTION OF GENTZEN-TYPE --
§ I. The languages of first order [13] --
§ 2. Inference rules and deductions [16] --
§ 3. Notions concerning deductions [25] --
§ 4. An alternative definition of the deductions [29] --
II. THE INVERSION PRINCIPLE --
§ i. Properties of the inference rules [32] --
i § 2. Reduction steps [35] --
III. NORMAL DEDUCTIONS IN CLASSICAL LOGIC --
§ i| Theorem on normal deductions [39] --
§ 2. The form of normal deductions [41] --
§ 3. Some further corollaries [44] --
IV. NORMAL DEDUCTIONS IN INTUITIONISTIC LOGIC --
§ i. Theorem on normal deductions [49] --
§ 2. The form of normal deductions [52] --
§ 3. Some further corollaries [54] --
V. SECOND ORDER LOGIC --
§ 1. Natural deduction for second order logic [63] --
§ 2. Normal deductions in ramified 2nd order logic [68] --
§ 3. The unprovability by finitary methods of the theorem on normal deductions for simple 2nd order logic [71] --
VI. MODAL LOGIC --
§ 1. Natural deduction for modal logic [74] --
§ 2. Essentially modal formulas [76] --
§ 3. Normal deductions in the S4-systems [78] --
§ 4. Normal deductions in C'S5 [80] --
VII. SOME OTHER CONCEPTS OF IMPLICATION --
§ i. Relevant implication [81] --
§ 2. Relevant implication extended by minimal and classical logic [83] --
§ 3. Rigorous implication [86] --
APPENDIX A. THE CALCULI OF SEQUENTS --
§ i. Definition of the calculi of sequents [88] --
§ 2. Connections between the calculi of sequents and the systems of natural deduction [90] --
§ 3. Gentzen’s Hauptsatz [91] --
APPENDIX B. ON A SET THEORY BY FITCH --
§ i. A demonstrably consistent set theory [94] --
§ 2. The relation of the system F to Fitch’s system [96] --
APPENDIX C. NOTES ON SOME OTHER VARIANTS OF NATURAL DEDUCTION --
§ i. The origin of natural deduction [98] --
§ 2. Variants of Gentzen-type systems [101] --
§ 3. Rules for existential instantiation [103] --
MR, 33 #1227
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