# A Systematic Approach to Canonicity in the Classical Sequent Calculus

@inproceedings{Chaudhuri2012ASA, title={A Systematic Approach to Canonicity in the Classical Sequent Calculus}, author={Kaustuv Chaudhuri and Stefan Hetzl and Dale Miller}, booktitle={CSL}, year={2012} }

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…

## 10 Citations

Expansion trees with cut

- Computer Science, MathematicsMathematical Structures in Computer Science
- 2019

This paper presents a new syntactic approach that directly extends Miller’s expansion trees by cuts and also covers non-prenex formulas and describes a cut-elimination procedure for the expansion trees with cut that is based on the natural reduction steps and shows that it is weakly normalizing.

Herbrand-Confluence

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2013

The main theorem is a confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing reduction lead to the same Herbrand-disjunction of a cut-free proof.

Herbrand-Confluence Stefan Hetzl and

- Mathematics, Computer Science
- 2013

The main theorem is a confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing reduction lead to the same Herbrand-disjunction of a cut-free proof.

Polarised Intermediate Representation of Lambda Calculus with Sums

- Mathematics2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
- 2015

An untyped representation-an intermediate calculus-for the λ-calculus with sums is proposed, based on the following principles: Computation is described as the reduction of pairs of an expression and a context; the context must be represented inside-out.

Which simple types have a unique inhabitant?

- Computer ScienceICFP
- 2015

A saturating focused logic that introduces irreducible cuts on positive types ``as soon as possible''.

Multi-Focusing on Extensional Rewriting with Sums

- Computer ScienceTLCA
- 2015

We propose a logical justification for the rewriting-based equivalence procedure for simply-typed lambda-terms with sums of Lindley. It relies on maximally multi-focused proofs, a notion of canonical…

Proof Search in Multi-Agent Dialogues for Modal Logic

- Computer Science, Philosophy
- 2018

Constructive modal logics, as a combination of intuitionistic propositional logic and classical modalLogics, describe a family of modal systems which are, compared to the classical variant, more restrictive concerning the validity of formulas.

Deciding equivalence with sums and the empty type

- MathematicsPOPL
- 2017

This paper proves the decidability of βη-equivalence in presence of the empty type, the fact that it coincides with contextual equivalence, and with set-theoretic equality in all finite models.

## References

SHOWING 1-10 OF 49 REFERENCES

Canonical Sequent Proofs via Multi-Focusing

- Mathematics, Computer ScienceIFIP TCS
- 2008

This paper recovers permutative canonicity directly in the cut-free sequent calculus by generalizing focused sequent proofs to admit multiple foci, and then considering the restricted class of maximally multi-focused proofs.

A Proof Calculus Which Reduces Syntactic Bureaucracy

- Computer Science, MathematicsRTA
- 2010

A logic-independent proof calculus, where proofs can be freely composed by connectives, and prove its basic properties, which allows to avoid certain types of syntactic bureaucracy inherent to all usual proof systems.

Logic Programming with Focusing Proofs in Linear Logic

- Computer ScienceJ. Log. Comput.
- 1992

It is shown that the syntactic restriction induced by LinLog is not performed at the cost of any expressive power: a mapping from full linear logic to LinLog, preserving focusing proofs, and analogous to the normalization to clausal form for classical logic, is presented.

A compact representation of proofs

- Computer ScienceStud Logica
- 1987

This paper is able to prove a strengthen form of the firstorder interpolation theorem as well as provide a correct description of Skolem functions and the Herbrand Universe.

A New Deconstructive Logic: Linear Logic

- Computer ScienceJ. Symb. Log.
- 1997

The method presented is powerful: it allows us to recover as fragments formalisms as seemingly different as Girard's LC and Parigot's λμ, FD, delineates other viable systems as well, and gives means to extend the Krivine/Leivant paradigm of ‘programming-with-proofs’ to classical logic.

Naming Proofs in Classical Propositional Logic

- Computer Science, MathematicsTLCA
- 2005

With the Boolean semiring, the theory of classical proof nets is presented, with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure, which gives a “Boolean” category, which is not a poset.

Focusing and polarization in linear, intuitionistic, and classical logics

- Computer ScienceTheor. Comput. Sci.
- 2009

A framework for defining logics

- Computer ScienceJACM
- 1993

The Edinburgh Logical Framework provides a means to define (or present) logics through a general treatment of syntax, rules, and proofs by means of a typed λ-calculus with dependent types, whereby each judgment is identified with the type of its proofs.