The New Normal: We Cannot Eliminate Cuts in Coinductive Calculi, But We Can Explore Them. Issue 6 (November 2020)

• Record Type: Journal Article
• Authors: Komendantskaya, Ekaterina; Rozplokhas, Dmitry; Basold, Henning
• Is Part Of: Theory and practice of logic programming. Volume 20:Issue 6(2020)
• Page Start: 990
• Page End: 1005
• Publication Date: 2020-11
• Subjects: Sequent Calculus, -- Horn Clauses, -- Coinduction, -- Cut Elimination, -- Theory Exploration; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068420000423
• Languages: English
• ISSNs: 1471-0684

Abstract

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 .