- Page 1 and 2: On Intuitionistic Linear Logic G.M.
- Page 3: Summary In this thesis we carry out
- Page 7: Acknowledgements Firstly, and above
- Page 11 and 12: Contents 1 Introduction 1 1 Backgro
- Page 13 and 14: List of Figures 2.1 Sequent Calculu
- Page 15 and 16: Chapter 1 Introduction 1 Background
- Page 17 and 18: §2. Overview of Logical Systems an
- Page 19 and 20: §5. Results 5 We show how all thre
- Page 21 and 22: Chapter 2 Proof Theory 1 Sequent Ca
- Page 23 and 24: §1. Sequent Calculus 9 (tR) Γ −
- Page 25 and 26: §1. Sequent Calculus 11 2. The cut
- Page 27 and 28: §1. Sequent Calculus 13 (c) (⊗R,
- Page 29 and 30: §1. Sequent Calculus 15 Let Π ′
- Page 31 and 32: §1. Sequent Calculus 17 (e) ⊗R.
- Page 33 and 34: §1. Sequent Calculus 19 We have by
- Page 35 and 36: §1. Sequent Calculus 21 (p) Contra
- Page 37 and 38: §2. Natural Deduction 23 1.3 Subfo
- Page 39 and 40: §2. Natural Deduction 25 The Contr
- Page 41 and 42: §2. Natural Deduction 27 proposal.
- Page 43 and 44: §2. Natural Deduction 29 It is pos
- Page 45 and 46: §2. Natural Deduction 31 • (&I)
- Page 47 and 48: §2. Natural Deduction 33 (We have
- Page 49 and 50: §2. Natural Deduction 35 • Commu
- Page 51 and 52: §2. Natural Deduction 37 commutes
- Page 53 and 54: §3. Axiomatic Formulation 39 Theor
- Page 55 and 56: §3. Axiomatic Formulation 41 An im
- Page 57 and 58: §4. Comparisons 43 • A proof π
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§4. Comparisons 45 • A proof π
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§4. Comparisons 47 is mapped to th
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§4. Comparisons 49 • A deduction
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§4. Comparisons 51 • A deduction
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§4. Comparisons 53 • A deduction
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§4. Comparisons 55 • A deduction
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§4. Comparisons 57 • A derivatio
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§5. Translations 59 If Γ = A1, .
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§5. Translations 61 • A deductio
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§5. Translations 63 which reduces
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§5. Translations 65 S : (A ⊃ (B
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Chapter 3 Term Assignment 1 The Cur
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§1. The Curry-Howard Correspondenc
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§2. Term Assignment for Sequent Ca
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§3. Linear Combinatory Logic 73 x:
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§3. Linear Combinatory Logic 75 IA
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§4. Reduction Rules 77 (λx: A.M)
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§4. Reduction Rules 79 (copy M as
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§4. Reduction Rules 81 promote (pr
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§4. Reduction Rules 83 • (−◦
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§4. Reduction Rules 85 • (Promot
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§4. Reduction Rules 87 • (⊕L,P
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§5. Properties of Reduction Rules
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§5. Properties of Reduction Rules
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§5. Properties of Reduction Rules
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§5. Properties of Reduction Rules
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§5. Properties of Reduction Rules
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§6. Compilation into Linear Combin
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§6. Compilation into Linear Combin
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§7. Translations 103 Γ ⊲ M: A
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Chapter 4 Categorical Analysis 1 Li
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§2. Categorical Semantics for Line
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§3. Analysing the Linear Term Calc
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§4. The Model for Intuitionistic L
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§4. The Model for Intuitionistic L
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§4. The Model for Intuitionistic L
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§4. The Model for Intuitionistic L
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§4. The Model for Intuitionistic L
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§6. Comparison: Seely’s Model 15
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§6. Comparison: Seely’s Model 15
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§6. Comparison: Seely’s Model 15
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§6. Comparison: Seely’s Model 15
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§6. Comparison: Seely’s Model 15
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§6. Comparison: Seely’s Model 16
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§7. Comparison: Lafont’s Model 1
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§7. Comparison: Lafont’s Model 1
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§7. Comparison: Lafont’s Model 1
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§7. Comparison: Lafont’s Model 1
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§8. Translations 171 ✒ ✠ C
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§8. Translations 173 A ✠ f ❅
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§8. Translations 175 (C, hC) hC
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§8. Translations 177 Let us consid
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Chapter 5 Conclusions and Further W
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§2. An Alternative Natural Deducti
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§3. Classical Linear Logic 183 Ide
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§4. Further Work 185 by-value or c
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Bibliography [1] S. Abramsky. Compu
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Bibliography 189 [36] R.P. Goré. C
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Bibliography 191 [76] A.S. Troelstr