Abstract
In this paper we define the concept of a profile, which is a characteristic clause set, corresponding to an LK-proof in first-order logic, which is invariant under rule permutations. It is shown (via cut-elimination) that the profile is even invariant under a large class of proof transformations (called “simple transformations”), which includes transformations to negation normal form. As proofs having the same profile show the same behavior w.r.t. cut-elimination (which can be formally defined via the method CERES), proofs obtained by simple transformations can be considered as equal in this sense. A comparison with related results based on proof nets is given: in particular it is shown that proofs having the same profile define a larger equivalence class than those having the same proof net.
Supported by the Austrian Science Fund (project no. P17995-N12).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baaz, M., Egly, U., Leitsch, A.: Normal Form Transformations. In: Handbook of Automated Reasoning, pp. 273–333 (2001)
Baaz, M., Leitsch, A.: Cut normal forms and proof complexity. Annals of Pure and Applied Logic 97, 127–177 (1999)
Baaz, M., Leitsch, A.: Cut-elimination and Redundancy-elimination by Resolution. Journal of Symbolic Computation 29(2), 149–176 (2000)
Baaz, M., Leitsch, A.: Towards a Clausal Analysis of Cut-Elimination. Journal of Symbolic Computation 41, 381–410 (2006)
Danos, V., Joinet, J.-B., Schellinx, H.: A New Deconstructive Logic: Linear Logic. Journal of Symbolic Logic 62(3), 755–807 (1997)
Danos, V., Joinet, J.-B., Schellinx, H.: Computational isomorphisms in classical logic. Theoretical Computer Science 294(3), 353–378 (2003)
Gentzen, G.: Untersuchungen über das logische Schließen. Mathematische Zeitschrift 39, 405–431 (1934–1935)
Kleene, S.C.: Permutability of Inferences in Gentzen’s Calculi LK and LJ. Memoirs of the American Mathematical Society 10, 1–26 (1952)
McKinley, R.: Categorical Model for First-Order Classical Proofs. PhD thesis, University of Bath (2006)
Robinson, E.: Proof Nets for Classical Logic. Journal of Logic and Computation 13(5), 777–797 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hetzl, S., Leitsch, A. (2007). Proof Transformations and Structural Invariance. In: Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. (eds) Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science(), vol 4460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75939-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-75939-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75938-6
Online ISBN: 978-3-540-75939-3
eBook Packages: Computer ScienceComputer Science (R0)