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.
Author(s): Dieter Probst, Peter Schuster (eds)
Series: Ontos Mathematical Logic, Volume 6
Publisher: De Gruyter
Year: 2016
Language: English
Pages: 374
Tags: History & Philosophy;Science & Math;Logic;Pure Mathematics;Mathematics;Science & Math;Epistemology;Philosophy;Politics & Social Sciences;Logic & Language;Philosophy;Politics & Social Sciences;Methodology;Philosophy;Politics & Social Sciences;Epistemology;Philosophy;Humanities;New, Used & Rental Textbooks;Specialty Boutique;Logic;Philosophy;Humanities;New, Used & Rental Textbooks;Specialty Boutique;Mathematics;Algebra & Trigonometry;Calculus;Geometry;Statistics;Science & Mathematics;New, Used & R
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
