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The New Normal: We Cannot Eliminate Cuts in Coinductive Calculi, But We Can Explore Them

Published online by Cambridge University Press:  22 September 2020

Ekaterina Komendantskaya Open the ORCID record for Ekaterina Komendantskaya [Opens in a new window] ,
Dmitry Rozplokhas  and
Henning Basold
Ekaterina Komendantskaya
Affiliation:
Heriot-Watt University, Edinburgh, Scotland, UK (e-mail: ek19@hw.ac.uk)
Dmitry Rozplokhas
Affiliation:
Jet Brains Research, St Petersburgh, Russia (e-mail: rozplokhas@gmail.com)
Henning Basold
Affiliation:
Leiden University, the Netherlands (e-mail: henning@basold.eu)
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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.

Keywords

Sequent CalculusHorn ClausesCoinductionCut EliminationTheory Exploration
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 6: 36th International Conference on Logic Programming Special Issue II , November 2020 , pp. 990 - 1005
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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