Concepts of Proof in Mathematics, Philosophy, and Computer Science

✍ Scribed by Dieter Probst, Peter Schuster (eds)

• Publisher: De Gruyter
• Year: 2016
• Tongue: English
• Leaves: 384
• Series: Ontos Mathematical Logic, Volume 6
• Category: Library

✦ Synopsis

This book provides the reader with research arising from the Humboldt-Kolleg 'Proof' held in Bern in fall 2013, which gathered leading experts actively involved with the concept 'proof' in philosophy, mathematics and computer science. This volume aims to do justice to the breadth and depth of the subject and presents relevant current conceptions and technical advances featuring 'proof' in those fields.

✦ Table of Contents

Dieter Probst and Peter Schuster
Introduction

Bahareh Afshari, Stefan Hetzl, and Graham E. Leigh
Herbrand Confluence for First-Order Proofs with Π₂-Cuts

Marco Benini
Proof-Oriented Categorical Semantics

Ulrich Berger, Kenji Miyamoto, Helmut Schwichtenberg, and Hideki Tsuiki
Logic for Gray-code Computation

Douglas S. Bridges
The Continuum Hypothesis Implies Excluded Middle

Ulrik Buchholtz, Gerhard Jäger, and Thomas Strahm
Theories of Proof-Theoretic Strength ψ(Γ_{Ω+1})

Thierry Coquand and Henri Lombardi
Some Remarks about Normal Rings

Kosta Došen
On Sets of Premises

Hajime Ishihara and Takako Nemoto
Non-Deterministic Inductive Defnitions and Fullness

Ioannis Kokkinis and Thomas Studer
Cyclic Proofs for Linear Temporal Logic

Roman Kuznets
Craig Interpolation via Hypersequents

Serafna Lapenta and Ioana Leuştean
A General View on Normal Form Theorems for Łukasiewicz Logic with Product

Maria Emilia Maietti and Giuseppe Rosolini
Relating Quotient Completions via Categorical Logic

Roman Murawski
Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics

Sara Negri and Jan von Plato
Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen’s Altitude Line Construction

Wolfram Pohlers
Hilbert’s Programme and Ordinal Analysis

Jan von Plato
Aristotle’s Deductive Logic: a Proof-Theoretical Study

Michael Rathjen
Remarks on Barr’s Theorem: Proofs in Geometric Theories

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