The new normal: we cannot eliminate cuts in coinductive calculi, but we can explore them
The new normal: we cannot eliminate cuts in coinductive calculi, but we can explore them
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. In this paper, we use coinductive Horn clause theories to show that cut is not eliminable in a coinductive extension of LJ, a system we call CLJ. We derive two further practical results from this study. We show that CoLP by Gupta et al. gives rise to cut-free proofs in CLJ with fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics for discovery of cut formulae in CLJ.
Coinduction, Cut Elimination, Horn Clauses, Sequent Calculus, Theory Exploration
990-1005
Komendantskaya, Ekaterina
f12d9c23-5589-40b8-bcf9-a04fe9dedf61
Rozplokhas, Dmitry
fa91cf31-3482-4ae4-a4ca-cab161416d1a
Basold, Henning
88ab5efa-e9d1-45aa-ad68-6cbf83089936
1 November 2020
Komendantskaya, Ekaterina
f12d9c23-5589-40b8-bcf9-a04fe9dedf61
Rozplokhas, Dmitry
fa91cf31-3482-4ae4-a4ca-cab161416d1a
Basold, Henning
88ab5efa-e9d1-45aa-ad68-6cbf83089936
Komendantskaya, Ekaterina, Rozplokhas, Dmitry and Basold, Henning
(2020)
The new normal: we cannot eliminate cuts in coinductive calculi, but we can explore them.
Theory and Practice of Logic Programming, 20 (6), .
(doi:10.1017/S1471068420000423).
Abstract
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. In this paper, we use coinductive Horn clause theories to show that cut is not eliminable in a coinductive extension of LJ, a system we call CLJ. We derive two further practical results from this study. We show that CoLP by Gupta et al. gives rise to cut-free proofs in CLJ with fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics for discovery of cut formulae in CLJ.
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Published date: 1 November 2020
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Keywords:
Coinduction, Cut Elimination, Horn Clauses, Sequent Calculus, Theory Exploration
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Local EPrints ID: 482785
URI: http://eprints.soton.ac.uk/id/eprint/482785
ISSN: 1471-0684
PURE UUID: d3e55356-adf4-4694-8192-1904cf64709d
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Date deposited: 12 Oct 2023 16:43
Last modified: 17 Mar 2024 05:09
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Author:
Ekaterina Komendantskaya
Author:
Dmitry Rozplokhas
Author:
Henning Basold
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