(Ebook) Proof Analysis: A Contribution to Hilbert's Last Problem by Sara Negri, Jan von Plato ISBN 9781107008953, 9781107417236, 1107008956, 1107417236

(Ebook) Proof Analysis: A Contribution to Hilbert's Last Problem by Sara Negri, Jan von Plato ISBN 9781107008953, 9781107417236, 1107008956, 1107417236

Main subject categories: • Proof theory • Hibert's last problem • Proof analysis • Proof theories based on natural deduction • Proof theories based on sequent calculus • Proof theories for geometric series • Proof theories for non-classical logicsThis 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.