Concepts of proof in mathematics, philosophy, and computer science

In the last decades, mathematical logic has developed into a technically quite sophisticated area of mathematics. Nevertheless, inspirations from philosophy and computer science continue to be important and noticeable. The series publishes conference proceedings as well as monographs written by lead...

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Hlavní autori: Probst, Dieter, Schuster, Peter
Médium: E-kniha Kniha
Jazyk:English
Vydavateľské údaje: Berlin De Gruyter 2016
Walter de Gruyter GmbH
Vydanie:1
Edícia:Ontos Mathematical Logic
Predmet:
Logic, Symbolic and mathematical
Mathematical Logic
Mathematics
MATHEMATICS / History & Philosophy
Mathematische Logik
Philosophie der Mathematik
PHILOSOPHY / Epistemology
PHILOSOPHY / Logic
PHILOSOPHY / Methodology
Philosophy of Mathematics
Proof theory
Theoretical Computer Science
Theoretische Informatik
Theoretische Informatik
Mathematical Logic
Philosophy of Mathematics
Mathematische Logik
Theoretical Computer Science
Philosophie der Mathematik
ISBN:1501510800, 9781501510809
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Obsah:
  • Intro -- Contents -- Introduction -- Herbrand Confluence for First-Order Proofs with π 2-Cuts -- Proof-Oriented Categorical Semantics -- Logic for Gray-code Computation -- The Continuum Hypothesis Implies Excluded Middle -- Theories of Proof-Theoretic Strength -- Some Remarks about Normal Rings -- On Sets of Premises -- Non-Deterministic Inductive Definitions and Fullness -- Cyclic Proofs for Linear Temporal Logic -- Craig Interpolation via Hypersequents -- A General View on Normal Form Theorems for Lukasiewicz Logic with Product -- Relating Quotient Completions via Categorical Logic -- Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics -- Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen's Altitude Line Construction -- Hilbert's Programme and Ordinal Analysis -- Aristotle's Deductive Logic: a Proof-Theoretical Study -- Remarks on Barr's Theorem: Proofs in Geometric Theories
  • Contents --
  • Preface --
  • Cut Elimination in Sequent Calculi with Implicit Contraction, with a Conjecture on the Origin of Gentzen’s Altitude Line Construction
  • Hajime Ishihara, Takako Nemoto --
  • Aristotle’s Deductive Logic: a Proof-Theoretical Study
  • On Sets of Premises
  • Jan von Plato --
  • Ulrik Buchholtz, Gerhard Jäger, Thomas Strahm --
  • Cyclic Proofs for Linear Temporal Logic
  • Ulrich Berger, Kenji Miyamoto, Helmut Schwichtenberg, Hideki Tsuiki --
  • Dieter Probst, Peter Schuster --
  • Maria Emilia Maietti, Giuseppe Rosolini --
  • Wolfram Pohlers --
  • Thierry Coquand, Henri Lombardi --
  • Michael Rathjen
  • Logic for Gray-code Computation
  • Some Remarks about Normal Rings
  • Hilbert’s Programme and Ordinal Analysis
  • Sara Negri, Jan von Plato --
  • Some Historical, Philosophical and Methodological Remarks on Proof in Mathematics
  • Roman Kuznets --
  • Non-Deterministic Inductive Definitions and Fullness
  • Theories of Proof-Theoretic Strength Ψ (ΓΩ +1)
  • Marco Benini --
  • Ioannis Kokkinis, Thomas Studer --
  • Roman Murawski --
  • Douglas S. Bridges --
  • Proof-Oriented Categorical Semantics
  • Introduction
  • Serafina Lapenta, Ioana Leuştean --
  • Relating Quotient Completions via Categorical Logic
  • Bahareh Afshari, Stefan Hetzl, Graham E. Leigh --
  • Frontmatter --
  • Craig Interpolation via Hypersequents
  • Kosta Došen --
  • The Continuum Hypothesis Implies Excluded Middle
  • Herbrand Confluence for First-Order Proofs with Π2-Cuts
  • A General View on Normal Form Theorems for Łukasiewicz Logic with Product
  • Remarks on Barr’s Theorem: Proofs in Geometric Theories