Concepts of proof in mathematics, philosophy, and computer science / Dieter Probst and Peter Schuster.

Format:

Book

Author/Creator:

Probst, Dieter, author.

Schuster, Peter, author.

Series:

Ontos Mathematical Logic, 2198-2341 ; Volume 6

Language:

English

Subjects (All):

Proof theory.

Mathematics.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (384 pages)

Place of Publication:

Berlin, [Germany] ; : De Gruyter, 2016.

Summary:

A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.

Contents:

Introduction

Herbrand Confluence for First-Order Proofs with Π2-Cuts

Proof-Oriented Categorical Semantics

Logic for Gray-code Computation

The Continuum Hypothesis Implies Excluded Middle

Theories of Proof-Theoretic Strength Ψ (ΓΩ +1)

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 Łukasiewicz 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

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

9781501502644

1501502646

9781501502620

150150262X

OCLC:

956701728