Beyersdorff, O and Kutz, O (2012) Proof complexity of non-classical logics. In: Bezhanishvili, N and Goranko, V, (eds.) Lectures on Logic and Computation ESSLLI 2010 Copenhagen, Denmark, August 2010, ESSLLI 2011, Ljubljana, Slovenia, August 2011, Selected Lecture Notes. Lecture Notes in Computer Science, 7388 . Springer Verlag , 1 - 54 . ISBN 978-3-642-31484-1
Proof complexity is an interdisciplinary area of research utilising techniques from logic, complexity, and combinatorics towards the main aim of understanding the complexity of theorem proving procedures. Traditionally, propositional proofs have been the main object of investigation in proof complexity. Due their richer expressivity and numerous applications within computer science, also non-classical logics have been intensively studied from a proof complexity perspective in the last decade, and a number of impressive results have been obtained. In these notes we give an introduction to this recent field of proof complexity of non-classical logics. We cover results from proof complexity of modal, intuitionistic, and non-monotonic logics. Some of the results are surveyed, but in addition we provide full details of a recent exponential lower bound for modal logics due to Hrubeš  and explain the complexity of several sequent calculi for default logic [16,13]. To make the text self-contained, we also include necessary background information on classical proof systems and non-classical logics.
|Copyright, Publisher and Additional Information:||© 2012, Springer Verlag. This is an author produced version of a chapter published in Lectures on Logic and Computation. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds)|
|Depositing User:||Symplectic Publications|
|Date Deposited:||03 Dec 2012 10:57|
|Last Modified:||17 Sep 2016 20:23|