Concepts of Proof in Mathematics, Philosophy, and Computer Science

Dieter Probst

ISBN 10: 1501510800 / ISBN 13: 9781501510809

Verlag: De Gruyter, US, 2016

Beschreibung

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.

Bestandsnummer des Verkäufers LU-9781501510809

Bibliografische Details

• Titel: Concepts of Proof in Mathematics, Philosophy, and Computer Science
• Verlag: De Gruyter, US
• Erscheinungsjahr: 2016
• Sprache: Englisch
• ISBN-10: 1501510800
• ISBN-13: 9781501510809
• Einband: Hardback
• Zustand: New
• Gewicht: 683 Gramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Dieter Probst, Inst. of Computer Science, U. Bern, Switzerland.Peter Schuster, Dept. of Computer Science, U. Verona, Italy.