## Advances in Natural Deduction: A Celebration of Dag Prawitz's WorkLuiz Carlos Pereira, Edward Haeusler, Valeria de Paiva This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism (itself a by-product of the work on natural deduction), via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. |

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### Contents

1 | |

2 Revisiting Zuckers Work on the Correspondence Between CutElimination and Normalisation | 31 |

3 Proofs Reasoning and the Metamorphosis of Logic | 51 |

The Missing Entity | 62 |

5 Paul Hertzs Systems of Propositions As a ProofTheoretical Conception of Logic | 93 |

6 On the Structure of Natural Deduction Derivations for Generally | 102 |

7 Type Theories from Barendregts Cube for Theorem Provers | 129 |

8 What is Propositional Logic a Theory of if Anything? | 145 |

9 Categorical Semantics of Linear Logic for All | 181 |

RoughSets Semantics and Proof Theory | 193 |

11 Decomposition of Reduction | 243 |

12 An Approach to General Proof Theory and a Conjecture of a Kind of Completeness of Intuitionistic Logic Revisited | 268 |

### Other editions - View all

Advances in Natural Deduction: A Celebration of Dag Prawitz's Work Luiz Carlos Pereira,edward haeusler,Valeria de Paiva No preview available - 2014 |

Advances in Natural Deduction: A Celebration of Dag Prawitz's Work Luiz Carlos Pereira,edward haeusler,Valeria de Paiva No preview available - 2016 |