Concepts of Proof in Mathematics, Philosophy, and Computer Science / / ed. by Dieter Probst, Peter Schuster.
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 prototyp...
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Superior document:  Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 

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Place / Publishing House:  Berlin ;, Boston : : De Gruyter, , [2016] ©2016 
Year of Publication:  2016 
Language:  English 
Series:  Ontos Mathematical Logic ,
6 
Online Access:  
Physical Description:  1 online resource (X, 374 p.) 
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Other title:  Frontmatter  Preface  Contents  Introduction  Herbrand Confluence for FirstOrder Proofs with Π2Cuts  ProofOriented Categorical Semantics  Logic for Graycode Computation  The Continuum Hypothesis Implies Excluded Middle  Theories of ProofTheoretic Strength Ψ (ΓΩ +1)  Some Remarks about Normal Rings  On Sets of Premises  NonDeterministic 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 ProofTheoretical Study  Remarks on Barr’s Theorem: Proofs in Geometric Theories 

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. 
Format:  Mode of access: Internet via World Wide Web. 
ISBN:  9781501502620 9783110762501 9783110701005 9783110485103 9783110485301 
ISSN:  21982341 ; 
DOI:  10.1515/9781501502620 
Access:  restricted access 
Hierarchical level:  Monograph 
Statement of Responsibility:  ed. by Dieter Probst, Peter Schuster. 