Concepts of Proof in Mathematics, Philosophy, and Computer Science

Concepts of Proof in Mathematics, Philosophy, and Computer Science 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. Additional ISBNs 9781501502620Concepts of Proof in Mathematics, Philosophy, and Computer Science 1st Edition and published by De Gruyter. ISBNs for Concepts of Proof in Mathematics, Philosophy, and Computer Science are 9781501502644, 1501502646 and the print ISBNs are 9781501510809, 1501510800. Additional ISBNs include 9781501502620.