000			04046nam a2200337 a 4500
005			20250918192221.0
008			130627s2011 enk b 001 0 eng
020			_a9781107008953 (hbk.) _cRM285.49
020			_a1107008956 (hbk.)
039		9	_a201311201037 _bzabidah _c201310301519 _drahah _y06-27-2013 _zrahah
040			_aDLC _cDLC _dYDX _dBTCTA _dYDXCP _dUKMGB _dCDX _dBWX _dDLC _dUKM
090			_aQA9.54.N477
090			_aQA9.54 _b.N477
100	1		_aNegri, Sara, _d1967-
245	1	0	_aProof analysis : _ba contribution to Hilbert's last problem / _cSara Negri, Jan von Plato.
260			_aCambridge, UK : _bCambridge University Press, _c2011.
300			_axi, 265 p. ; _c26 cm.
504			_aIncludes bibliographical references and index.
520			_a'This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians'-- _cProvided by publisher.
520			_a'We shall discuss the notion of proof and then present an introductory example of the analysis of the structure of proofs. The contents of the book are outlined in the third and last section of this chapter. 1.1 The idea of a proof A proof in logic and mathematics is, traditionally, a deductive argument from some given assumptions to a conclusion. Proofs are meant to present conclusive evidence in the sense that the truth of the conclusion should follow necessarily from the truth of the assumptions. Proofs must be, in principle, communicable in every detail, so that their correctness can be checked. Detailed proofs are a means of presentation that need not follow in anyway the steps in finding things out. Still, it would be useful if there was a natural way from the latter steps to a proof, and equally useful if proofs also suggested the way the truths behind them were discovered. The presentation of proofs as deductive arguments began in ancient Greek axiomatic geometry. It took Gottlob Frege in 1879 to realize that mere axioms and definitions are not enough, but that also the logical steps that combine axioms into a proof have to be made, and indeed can be made, explicit. To this purpose, Frege formulated logic itself as an axiomatic discipline, completed with just two rules of inference for combining logical axioms. Axiomatic logic of the Fregean sort was studied and developed by Bert-rand Russell, and later by David Hilbert and Paul Bernays and their students, in the first three decades of the twentieth century. Gradually logic came to be seen as a formal calculus instead of a system of reasoning: the language of logic was formalized and its rules of inference taken as part of an inductive definition of the class of formally provable formulas in the calculus'-- _cProvided by publisher.
650		0	_aProof theory.
700	1		_aVon Plato, Jan.
907			_a.b15672530 _b2019-11-12 _c2019-11-12
942			_c01 _n0 _kQA9.54.N477
914			_avtls003533921
990			_aza
991			_aFakulti Sains Sosial & Kemanusiaan
998			_at _b2013-01-06 _cm _da _feng _genk _y0 _z.b15672530
999			_c549922 _d549922