Research and Publications

Edition Projects

• The Collected Works of Rudolf Carnap
• Paul Bernays: Philosopher of Mathematics
• David Hilbert and Paul Bernays, Grundlagen der Mathematik

Edited Collection

• Mathematical Applications in Philosophy, special issue of The Review of Symbolic Logic 1 (September 2008). (Co-edited with Aldo Antonelli and Alasdair Urquhart.)

Papers by Subject

Click on links for abstracts, review information, and download links. See below for a list of publications in chronological order

History of Logic The development of mathematical logic from Russell to Tarski Kurt Gödel and computability theory The practice of finitism: Epsilon calculus and consistency proofs in Hilbert's Program Hilbert's "Verunglückter Beweis," the first epsilon theorem, and consistency proofs Completeness before Post: Bernays, Hilbert, and the development of propositional logic Kurt Gödel, paper on the incompleteness theorems (1931)	Theory of Proofs The epsilon calculus and Herbrand complexity The epsilon calculus Generalizing theorems in real closed fields Note on generalizing theorems in algebraically closed fields Short proofs of tautologies using the schema of equivalence Algorithmic structuring of cut-free proofs
Philosophy of Mathematics Hilbert’s program then and now Gödel's first incompleteness theorem and mathematical instrumentalism Critical study of Michael Potter's Reason's Nearest Kin Numbers and functions in Hilbert's finitism Hilbert's Program Hilbert's Finitism. Historical, Philosophical, and Metamathematical Perspectives	Gödel Logics First-order Gödel Logics Characterization of the axiomatizable prenex fragments of first-order Gödel logics Quantified propositional Gödel logic Hypersequents and the proof theory of intuitionistic fuzzy logic Compact propositional Gödel logics Incompleteness of an infinite-valued first-order Gödel logic and of some temporal logics of programs
Finite-valued Logic Labeled calculi and finite-valued logics Approximating propositional calculi by finite-valued logics Systematic construction of natural deduction systems for many-valued logics Elimination of cuts in first-order many-valued logics Proof Theory of Finite-Valued Logics	Other Logic Effective Finite-Valued Approximations of General Propositional Logics Decidability of quantified propositional intuitionistic logic and S4 on trees of height and arity ≤ω A complete first-order temporal logic of time with gaps Tableaux for reasoning about atomic updates
Other Writings Vagueness, Logic and Use: Four Experimental Studies on Vagueness

Papers Chronologically

Work in Progress

1. Gödel's first incompleteness theorem and mathematical instrumentalism.

Published Articles and Articles in Press

1. Vagueness, logic and use: Four experimental studies on vagueness. Mind and Language 26 (2011) 540–573. (with Phil Serchuk and Ian Hargreaves)
2. The development of mathematical logic from Russell to Tarski: 1900-1935. In: Leila Haaparanta, ed., The History of Modern Logic. New York and Oxford: Oxford University Press, 2009, pp. 324-479. (with Paolo Mancosu and Calixto Badesa)
3. Effective Finite-Valued Approximations of General Propositional Logics. Avron, Arnon; Dershowitz, Nachum; Rabinovich, Alexander (Eds.). Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Lecture Notes in Computer Science 4800. Berlin: Springer, 2008. 107-129 (with Matthias Baaz)
4. First-order Gödel Logics. Annals of Pure and Applied Logic 147 (2007) 23-47 (with Matthias Baaz and Norbert Preining)
5. Kurt Gödel and computability theory. Logical Approaches to Computational Barriers Second Conference on Computability in Europe, CiE 2006, Swansea. Proceedings. LNCS 3988 (Springer, Berlin, 2006) 575-58
6. The epsilon calculus and Herbrand complexity. Studia Logica 82 (2006) 133-155 (with Georg Moser).
7. Hilbert’s program then and now. In: Dale Jacquette, ed., Philosophy of Logic (Elsevier, Amsterdam, 2006), 411-447.
8. Critical study of Michael Potter's Reason's Nearest Kin. Notre Dame J. Formal Logic 46 (2005) 503–513.
9. Kurt Gödel, paper on the incompleteness theorems (1931), In: Ivor Grattan-Guinness, ed., Landmark Writings in Mathematics (North-Holland, Amsterdam, 2004) 917–925
10. Decidability of quantified propositional intuitionistic logic and S4 on trees of height and arity ≤ ω, Journal of Philosophical Logic 33 (2004) 155–164.
11. Hilbert's "Verunglückter Beweis," the first epsilon theorem, and consistency proofs, History and Philosophy of Logic 25 (2004) 79–94.
12. The practice of finitism: Epsilon calculus and consistency proofs in Hilbert's Program, Synthese 137 (2003) 211-259.
13. Hilbert's Program, Stanford Encyclopedia of Philosophy, 2003. http://plato.stanford.edu/entries/hilbert-program/
14. Characterization of the axiomatizable prenex fragments of first-order Gödel logics, 33rd International Symposium on Multiple-valued Logic. Proceedings. Tokyo, May 16-19, 2003 (IEEE Computer Society Press, 2003) 175-180 (with Matthias Baaz and Norbert Preining).
15. The epsilon calculus, Stanford Encyclopedia of Philosophy, 2002. http://plato.stanford.edu/entries/epsilon-calculus/ (with Jeremy Avigad)
16. Tableaux for reasoning about atomic updates, Logic for Programming, Artificial Intelligence, and Reasoning. 8th International Conference, LPAR 2001. Proceedings, LNAI 2250. (Springer, Berlin, 2001) 639–653 (with Christian G. Fermüller, Georg Moser).
17. Quantified propositional Gödel logic, Voronkov, Andrei, and Michel Parigot (eds.), Logic for Programming and Automated Reasoning. 7th International Conference, LPAR 2000. Proceedings, LNAI 1955 (Springer, Berlin, 2000) 240–256 (Matthias Baaz, Agata Ciabattoni)
18. Hypersequents and the proof theory of intuitionistic fuzzy logic, Clote, Peter G., and Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Fischbachau, Germany, August 21-26, 2000. Proceedings. (Springer, Berlin, 2000) 187–201. (with Matthias Baaz)
19. Completeness before Post: Bernays, Hilbert, and the development of propositional logic, Bulletin of Symbolic Logic 5 (1999) 331–366.
20. Numbers and functions in Hilbert's finitism, Taiwanese Journal for Philosophy and History of Science 10 (1998) 33–60 (invited paper, special issue on philosophy of mathematics edited by Charles Chihara)
21. Labeled calculi and finite-valued logics, Studia Logica 61 (1998) 7–33 (with Matthias Baaz, Christian G. Fermüller, Gernot Salzer)
22. Note on generalizing theorems in algebraically closed fields, Archive for Mathematical Logic 37 (1998) 297–307 (with Matthias Baaz)
23. Compact propositional Gödel logics, 28th International Symposium on Multiple Valued Logic. May 1998, Fukuoka, Japan. Proceedings (IEEE Computer Society Press, Los Alamitos, 1998) 108–113 (with Matthias Baaz)
24. A complete first-order temporal logic of time with gaps, Theoretical Computer Science 160 (1996) 241–270 (with Matthias Baaz, Alexander Leitsch)
25. Incompleteness of an infinite-valued first-order Gödel logic and of some temporal logics of programs, Computer Science Logic. 9th Workshop, CSL'95. Paderborn. Selected Papers (Springer, Berlin, 1996) 1–15 (with Matthias Baaz, Alexander Leitsch)
26. Generalizing theorems in real closed fields, Annals of Pure and Applied Logic 75 (1995) 3–23 (with Matthias Baaz)
27. Elimination of cuts in first-order many-valued logics, Journal of Information Processing and Cybernetics 29 (1994) 333–355 (with Matthias Baaz, Christian G. Fermüller)
28. Approximating propositional calculi by finite-valued logics, 24th International Symposium on Multiple Valued Logic. Boston. Proceedings (IEEE Press, Los Alamitos, 1994) 257–263 (with Matthias Baaz)
29. Short proofs of tautologies using the schema of equivalence, Computer Science Logic. 7th Workshop, CSL'93. Swansea. Selected Papers (Springer, Berlin, 1994) 33–35 (with Matthias Baaz)
30. Systematic construction of natural deduction systems for many-valued logics, 23rd International Symposium on Multiple Valued Logic. Sacramento. Proceedings (IEEE Press, Los Alamitos, 1993) 208–213 (with Matthias Baaz, Christian G. Fermüller)
31. Dual systems of sequents and tableaux, Workshop on Tableau-based Deduction, Marseille, 1993. Bulletin of the EATCS 51 (1993) 192–197 (with Matthias Baaz, Christian G. Fermüller)
32. Algorithmic structuring of cut-free proofs, Computer Science Logic. 6th Workshop, CSL '92. San Miniato. Selected Papers (Springer, Berlin, 1993) 29–42 (with Matthias Baaz)

Reviews and Reports

1. (Review) Review of Computability and Logic, 4th Edition, by George Boolos, John Burgess, and Richard Jeffrey (Cambridge, 2002). Bulletin of Symbolic Logic 9 (2003) 520-521
2. (Review) Review of Computability. Computable Functions, Logic, and the Foundations of Mathematics, 2nd Edition, by Richard L. Epstein and Walter A. Carnielli (Wadsworth, 2000). History and Philosophy of Logic 23 (2002) 67–70.
3. (Review) Review of Many-valued Logics: 1. Theoretical Foundations, by Leonard Bolc and Piotr Borowik (Springer, Berlin, 1991), Journal of Applied Non-Classical Logics 4 (1994) 215–220 (with Petr Hájek)
4. (Report) Art/ificial Intelligence. A Short Bibliography on AI and the Arts, ÖFAI Report TR-90-14, Austrian Research Institute for Artificial Intelligence, 1990 (with Gerhard Widmer, Robert Trappl)

Theses

1. Hilbert's Finitism. Historical, Philosophical, and Metamathematical Perspectives, Dissertation, University of California, Berkeley, Spring 2001
2. Proof Theory of Finite-Valued Logics, Diploma Thesis, Technische Universität Wien, Vienna, 1993