Proof analysis :
Negri, Sara, 1967-
Proof analysis : a contribution to Hilbert's last problem / Sara Negri, Jan von Plato. - Cambridge : Cambridge University Press, 2011. - 1 online resource (xi, 265 pages) : digital, PDF file(s).
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Hilbert's Last Problem -- Proof Systems Based on Natural Deduction -- Rules of proof: natural deduction -- Axiomatic systems -- Order and lattice theory -- Theories with existence axioms -- Proof Systems Based on Sequent Calculus -- Rules of proof: sequent calculus -- Linear order -- Proof Systems for Geometric Theories -- Geometric theories -- Classical and intuitionistic axiomatics -- Proof analysis in elementary geometry -- Proof Systems for Nonclassical Logics -- Modal logic -- Quantified modal logic, provability logic, and so on; Prologue: Introduction; Part I. Part II. Part III. Part IV. Bibliography; Index of names; Index of subjects.
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.
9781139003513 (ebook)
Proof theory.
QA9.54 / .N438 2011
511.3/6
Proof analysis : a contribution to Hilbert's last problem / Sara Negri, Jan von Plato. - Cambridge : Cambridge University Press, 2011. - 1 online resource (xi, 265 pages) : digital, PDF file(s).
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Hilbert's Last Problem -- Proof Systems Based on Natural Deduction -- Rules of proof: natural deduction -- Axiomatic systems -- Order and lattice theory -- Theories with existence axioms -- Proof Systems Based on Sequent Calculus -- Rules of proof: sequent calculus -- Linear order -- Proof Systems for Geometric Theories -- Geometric theories -- Classical and intuitionistic axiomatics -- Proof analysis in elementary geometry -- Proof Systems for Nonclassical Logics -- Modal logic -- Quantified modal logic, provability logic, and so on; Prologue: Introduction; Part I. Part II. Part III. Part IV. Bibliography; Index of names; Index of subjects.
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.
9781139003513 (ebook)
Proof theory.
QA9.54 / .N438 2011
511.3/6