LEADER 04046oam 2200637I 450 001 9910796687303321 005 20230808202658.0 010 $a1-5015-0264-6$b(electronic book) 010 $a1-5015-0262-X 024 7 $a10.1515/9781501502620 035 $a(CKB)3850000000000638 035 $a(EBL)4644584 035 $a(MiAaPQ)EBC4644584 035 $a(DE-B1597)451552 035 $a(OCoLC)956701728 035 $a(DE-B1597)9781501502620 035 $a(Au-PeEL)EBL4644584 035 $a(CaPaEBR)ebr11247831 035 $a(CaONFJC)MIL947521 035 $a(OCoLC)958120545 035 $a(EXLCZ)993850000000000638 100 $a20160903h20162016 uy 0 101 0 $aeng 135 $aurcnu|||uuuuu 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConcepts of proof in mathematics, philosophy, and computer science /$fDieter Probst and Peter Schuster 210 1$aBerlin, [Germany] ; :$cDe Gruyter,$d2016. 210 4$dİ2016 215 $a1 online resource (384 pages) 225 1 $aOntos Mathematical Logic,$x2198-2341 ;$vVolume 6 300 $aDescription based upon print version of record. 320 $aIncludes bibliographical references at the end of each chapters. 327 $aIntroduction -- Herbrand Confluence for First-Order Proofs with ?2-Cuts -- Proof-Oriented Categorical Semantics -- Logic for Gray-code Computation -- The Continuum Hypothesis Implies Excluded Middle -- Theories of Proof-Theoretic Strength ? (?? +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 ?ukasiewicz 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 330 $aA 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. 606 $aProof theory 606 $aMathematics 606 $aLogic, Symbolic and mathematical 610 $aMathematical Logic. 610 $aPhilosophy of Mathematics. 610 $aTheoretical Computer Science. 615 0$aProof theory. 615 0$aMathematics. 615 0$aLogic, Symbolic and mathematical. 676 $a511.36 700 $aProbst$b Dieter$01536153 702 $aSchuster$b Peter 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 801 2$b6680 906 $aBOOK 912 $a9910796687303321 996 $aConcepts of proof in mathematics, philosophy, and computer science$93784712 997 $aUNINA