Proof Compression with the CIRes Method [Abstract]

Bruno Woltzenlogel Paleo 1, *
* Auteur correspondant
1 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : It is well-known that eliminating cuts from sequent calculus proofs frequently increases the size and length of proofs. In the worst case, cut-elimination can produce non-elementarily larger and longer proofs [3, 2]. Given this fact, it is natural to attempt to devise methods that could introduce cuts and compress cut-free proofs. However, this has been a notoriously difficult task. Indeed, the problem of answering, given a proof φ and a number l such that l ≤ length(φ), whether there is a proof ψ (possibly with cuts) of the same theorem and such that length(ψ) < l is known to be undecidable [1]. Besides compression, cut-introduction can also be used for structuring and extracting interesting concepts from proofs. In the formalization of mathematical proofs, lemmas correspond to cuts, and hence the automatic introduction of cuts is, in a formal level, the automatic discovery of lemmas that are potentially useful for structuring mathematical knowledge. This talk presents a new method for the introduction of atomic cuts, CIRes, and shows that it is capable of providing exponential compression in the length of proofs. This compression is illustrated by an example sequence of proofs encoding computations of Fibonacci numbers.
Type de document :
Communication dans un congrès
Computability in Europa, Jun 2010, Ponta Delgada, Portugal
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https://hal.archives-ouvertes.fr/hal-00545496
Contributeur : Bruno Woltzenlogel Paleo <>
Soumis le : vendredi 10 décembre 2010 - 13:55:35
Dernière modification le : jeudi 11 janvier 2018 - 06:23:13

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  • HAL Id : hal-00545496, version 1

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Bruno Woltzenlogel Paleo. Proof Compression with the CIRes Method [Abstract]. Computability in Europa, Jun 2010, Ponta Delgada, Portugal. 〈hal-00545496〉

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