Ciabattoni, Agata;
Lang, Timo;
Ramanayake, Revantha;
(2023)
Cut-restriction: from cuts to analytic cuts.
In:
2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).
IEEE: Boston, MA, USA.
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Abstract
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations into decidability, complexity, disjunction property, interpolation, and more. Unfortunately cut-elimination does not hold for the sequent calculi of most non-classical logics. It is well-known that the key to applications is the subformula property (a typical consequence of cut-elimination) rather than cut-elimination itself. With this in mind, we introduce cut-restriction, a procedure to restrict arbitrary cuts to analytic cuts (when elimination is not possible). The algorithm applies to all sequent calculi satisfying language-independent and simple-to-check conditions, and it is obtained by adapting age-old cut-elimination. Our work encompasses existing results in a uniform way, subsumes Gentzen’s cut-elimination, and establishes new analytic cut properties.
Type: | Proceedings paper |
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Title: | Cut-restriction: from cuts to analytic cuts |
Event: | 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) |
Location: | Boston Univ, Boston, MA |
Dates: | 26 Jun 2023 - 29 Jun 2023 |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1109/LICS56636.2023.10175785 |
Publisher version: | https://doi.org/10.1109/LICS56636.2023.10175785 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Computer science, Interpolation, Sufficient conditions, Semantics, Calculus, Complexity theory, Standards |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
URI: | https://discovery.ucl.ac.uk/id/eprint/10177712 |
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