The Journal of Symbolic Logic (4)
Association for Symbolic Logic (4)
Lecture Notes in Logic (8)
UNSOUND INFERENCES MAKE PROOFS SHORTER
JUAN P. AGUILERA, MATTHIAS BAAZ
Journal: The Journal of Symbolic Logic / Volume 84 / Issue 1 / March 2019
We give examples of calculi that extend Gentzen's sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proofs therein are nonelementarily shorter than LK-proofs.
By Matthias Baaz, Vienna University of Technology, Sy Friedman, University of Vienna, Jan Krajíček, Academy of Sciences of the Czech Republic, Prague
Edited by Matthias Baaz, Technische Universität Wien, Austria, Sy-David Friedman, Jan Krajíček, Academy of Sciences of the Czech Republic, Prague
Book: Logic Colloquium '01
Published online: 31 March 2017, pp v-vi
The 2001 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium 2001 was held at the Vienna University of Technology in Vienna, Austria August 6–11, 2001. It was organized by the International Kurt Godel Society on the occasion of the 70th anniversary of Godel's famous publication Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I.
The program of the Logic Colloquium 2001 included 17 invited one hour plenary addresses, 2 tutorials and 17 invited half-hour lecturers in parallel special sessions on Set Theory, ModelTheory, Proof Theory and Proof Search, Computability Theory, Philosophy and History of Logic, Computer Science and Complexity Theory. In addition, there were 126 contributed talks plus 36 papers presented by title. The number of registered participants was 249 coming from around 25 countries.
The tutorial short courses were given by Alexander Leitsch, Resolution theorem proving, and Itay Neeman, Determinacy of long games.
Invited plenary addresses were given by Toshiyasu Arai, Wellfoundedness proofs in reflecting universes; SteveAwodey,Modal and intensional types in categorical logic; James Cummings, Squares, scales and reflection; RodDowney, Calibrating randomness; Harvey Friedman, Recent incompleteness; Warren Goldfarb, Gödel and Carnap: influence and opposition; Olga Kharlampovich, First order properties of free groups; Julia Knight, Quantifiers and complexity; Michiel van Lambalgen, Moschovakis's notion of meaning as applied to linguistics; Chris Miller, Tameness phenomena in expansions of the field of real numbers; RanRaz, Resolution Lower bounds for the weak pigeonhole principle; Saharon Shelah, (Nn, N0) may fail N0–compactness; Jouko Vaananen, Models, trees and infinitary back-and-forth; FrankWagner, Simplicity theory; Stan Wainer, Provable recursiveness and complexity.
Special plenary addresses commemorating the anniversary of Godel's incompleteness theorem were given by Georg Kreisel, A consumer's (re)view around higher infinites, and Gaisi Takeuti, Incompleteness theorem and its frontier.
The Programm Committee consisted of M. Arslanov, M. Baaz, W. Buchholz, S. Friedman, D. Isaacson, C. Jockusch, J. Krajíček (Chair), L. Newelski (resigned April 2000), J. Paris, J.-P. Ressayre, L. van den Dries, B. Velickovic, A. Visser.
The editors invited all pleanry, section and tutorial speakers to contribute to the proceedings. The present volume contains 19 papers. All papers were refereed. We appreciated very much the help of the referees (whose names we do not present for obvious reasons).
Published online: 31 March 2017, pp 87-88
Logic Colloquium '01
Edited by Matthias Baaz, Sy-David Friedman, Jan Krajíček
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twentieth publication in the Lecture Notes in Logic series, contains the proceedings of the 2001 European Summer Meeting of the Association for Symbolic Logic, held at the Vienna University of Technology. Two long articles present accessible expositions on resolution theorem proving and the determinacy of long games. The remaining articles cover separate research topics in many areas of mathematical logic, including applications in computer science, proof theory, set theory, model theory, computability theory, linguistics and aspects of philosophy. This collection will interest not only mathematical logicians but also philosophical logicians, historians of logic, computer scientists, formal linguists and mathematicians working in algebra, abstract analysis and topology.
An Axiomatization of Quantified Propositional Gödel Logic Using the Takeuti-Titani Rule
By Matthias Baaz, Technische Universität, Helmut Veith, Technische Universität
Edited by Samuel R. Buss, University of California, San Diego, Petr Hájek, Academy of Sciences of the Czech Republic, Prague, Pavel Pudlák, Academy of Sciences of the Czech Republic, Prague
Published online: 31 March 2017, pp 91-104
Published online: 31 March 2017, pp vii-viii
Published online: 31 March 2017, pp 1-2
Published online: 31 March 2017, pp i-iv
Infinite-valued G?del Logics with 0-1-Projections and Relativizations
from Part I - Invited Papers
By Matthias Baaz, Technische Universitat Wien
Edited by Petr Hájek, Academy of Sciences of the Czech Republic, Prague
Book: Gödel '96
Print publication: 02 March 2017, pp 23-33
On the complexity of proof deskolemization
Matthias Baaz, Stefan Hetzl, Daniel Weller
Journal: The Journal of Symbolic Logic / Volume 77 / Issue 2 / June 2012
We consider the following problem: Given a proof of the Skolemization of a formula F, what is the length of the shortest proof of F? For the restriction of this question to cut-free proofs we prove corresponding exponential upper and lower bounds.
I - Historical Context: Gödel's Contributions and Accomplishments
Edited by Matthias Baaz, Technische Universität Wien, Austria, Christos H. Papadimitriou, University of California, Berkeley, Hilary W. Putnam, Harvard University, Massachusetts, Dana S. Scott, Carnegie Mellon University, Pennsylvania, Charles L. Harper, Jr
Book: Kurt Gödel and the Foundations of Mathematics
Print publication: 06 June 2011, pp 1-2
II - A Wider Vision: The Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work
Print publication: 06 June 2011, pp 253-254
Gödel and the Human Mind
Print publication: 06 June 2011, pp xv-xvi
Kurt Gödel and the Foundations of Mathematics: Horizons of Truth is the culmination of a creative research initiative coorganized by the Kurt Gödel Society, Vienna; the Institute for Experimental Physics; the Kurt Gödel Research Center; the Institute Vienna Circle; the Vienna University of Technology; the Austrian Academy of Sciences; and the Anton Zeilinger Group at the University of Vienna, where the Gödel centenary celebratory symposium "Horizons of Truth: Logics, Foundations of Mathematics, and the Quest for Understanding the Nature of Knowledge" was held from April 27 to April 29, 2006.
More than twenty invited world-renowned researchers in the fields of mathematics, logic, computer science, physics, philosophy, theology, and the history of science attended the symposium, giving the participants the remarkable opportunity to present their ideas about Gödel's work and its influence on various areas of intellectual endeavor. These fascinating interdisciplinary lectures provided new insights into Gödel's life and work and their implications for future generations of researchers.
The interaction among international scholars who only rarely, if ever, have the opportunity to hold discussions in the same room – and some of whom almost never write articles – has produced a book that contains chapters expanded and developed to take advantage of the rich intellectual exchange that took place in Vienna. Written by some of the most renowned figures of the scientific and academic world, the resulting volume is an opus of current research and thinking that is built on the work and inspiration of Gödel.
Gödel's Legacy: A Historical Perspective
Print publication: 06 June 2011, pp 55-56
Print publication: 06 June 2011, pp xi-xii
Gödel and the Higher Infinite
Print publication: 06 June 2011, pp i-vi
Gödel and Computer Science
Print publication: 06 June 2011, pp vii-x