Skip to Main content Skip to Navigation
Conference papers

A Systematic Approach to Canonicity in the Classical Sequent Calculus

Kaustuv Chaudhuri 1 Stefan Hetzl 1 Dale Miller 1, 2 
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : The sequent calculus is often criticized for requiring proofs to contain large amounts of low-level syntactic details that can obscure the essence of a given proof. Because each inference rule introduces only a single connective, sequent proofs can separate closely related steps---such as instantiating a block of quantifiers---by irrelevant noise. Moreover, the sequential nature of sequent proofs forces proof steps that are syntactically non-interfering and permutable to nevertheless be written in some arbitrary order. The sequent calculus thus lacks a notion of canonicity: proofs that should be considered essentially the same may not have a common syntactic form. To fix this problem, many researchers have proposed replacing the sequent calculus with proof structures that are more parallel or geometric. Proof-nets, matings, and atomic flows are examples of such revolutionary formalisms. We propose, instead, an evolutionary approach to recover canonicity within the sequent calculus, which we illustrate for classical first-order logic. The essential element of our approach is the use of a multi-focused sequent calculus as the means of abstracting away the details from classical cut-free sequent proofs. We show that, among the multi-focused proofs, the maximally multi-focused proofs that make the foci as parallel as possible are canonical. Moreover, such proofs are isomorphic to expansion proofs---a well known, minimalistic, and parallel generalization of Herbrand disjunctions---for classical first-order logic. This technique is a systematic way to recover the desired essence of any sequent proof without abandoning the sequent calculus.
Document type :
Conference papers
Complete list of metadata

Cited literature [30 references]  Display  Hide  Download
Contributor : Kaustuv Chaudhuri Connect in order to contact the contributor
Submitted on : Thursday, January 10, 2013 - 2:31:21 PM
Last modification on : Thursday, January 20, 2022 - 5:30:47 PM
Long-term archiving on: : Thursday, April 11, 2013 - 4:05:42 AM


Files produced by the author(s)




Kaustuv Chaudhuri, Stefan Hetzl, Dale Miller. A Systematic Approach to Canonicity in the Classical Sequent Calculus. 21st EACSL Annual Conference on Computer Science Logic, Sep 2012, Fontainebleau, France. pp.183-197, ⟨10.4230/LIPIcs.CSL.2012.183⟩. ⟨hal-00772396⟩



Record views


Files downloads