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).
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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
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DOI: https://doi.org/10.1007/978-3-540-75939-3_13
Publisher Name: Springer, Berlin, Heidelberg
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