# A multi-focused proof system isomorphic to expansion proofs

@article{Chaudhuri2016AMP, title={A multi-focused proof system isomorphic to expansion proofs}, author={Kaustuv Chaudhuri and Stefan Hetzl and Dale Miller}, journal={J. Log. Comput.}, year={2016}, volume={26}, pages={577-603} }

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…

## 21 Citations

From focussed proof systems to complexity bounds

- Computer Science
- 2016

A notion of ‘over-focussing’ that admits non-branching invertible rules during synchronous phases is proposed, due to the fact that deterministic computations can equally be carried out by a nondeterministic machine.

Alternating time bounds from variants of focussed proof systems Intuitionistic logic and the polynomial hierarchy

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- 2017

A notion of ‘over-focussing’ that admits non-branching invertible rules during synchronous phases is proposed, due to the fact that deterministic computations can equally be carried out by a nondeterministic machine.

Focused and Synthetic Nested Sequents (Extended Technical Report)

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- 2016

A focused cut-elimination theorem for focused nested sequents is among the key contributions, which improves the reach of focusing to the most commonly studied modal logics, the logics of the modal S5 cube.

Modular normalisation of classical proofs

- Philosophy
- 2019

A local cycle removal procedure through reductions on merge contractions is shown that ensures that proofs can be decomposed—that contractions can be pushed to the bottom of a proof—in a straightforward way.

Herbrand Proofs and Expansion Proofs as Decomposed Proofs

- Mathematics, PhilosophyJ. Log. Comput.
- 2020

This paper constructs simple deep inference systems for first-order logic, both with and without cut, such that ‘decomposed’ proofs—proofs where the contractive and non-contractive behaviour of the proof is separated—in each system correspond to either expansion proofs or Herbrand proofs.

A Semantic Framework for Proof Evidence

- Computer Science, MathematicsJournal of Automated Reasoning
- 2016

The foundational proof certificates (FPC) framework is proposed, which allows both producers of proof certificates and the checkers of those certificates to have a clear formal definition of the semantics of a wide variety of proof evidence.

A general proof certification framework for modal logic

- Computer ScienceMathematical Structures in Computer Science
- 2019

This work proposes here a general framework for checking modal proofs using a classical focused sequent calculus as a kernel and presents the implementation of the framework in a Prolog-like language and shows how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms.

Modal proof theory through a focused telescope

- Computer Science
- 2018

In this thesis, we use in two ways the concept of synthetic inference rules that can be obtained from a focused proof system; from one side of the “telescope”, focusing allows us to analyse the…

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- Computer ScienceTYPES
- 2020

This paper implements in Elpi a proof checker for first-order intuitionistic logic and demonstrates how proof certificates can be supplied by external Coq provers and then elaborated into the fully detailed proof terms that can be checked by the Coq kernel.

Applications of Foundational Proof Certificates in theorem proving. (Applications des Certificats de Preuve Fondamentaux à la démonstration automatique de théorèmes)

- Computer Science, Mathematics
- 2017

This thesis extends initial results in certification of first-order proofs in several directions and applies developments to fully certify results produced by two families of standard automated theorem provers: resolution- and satisfiability-based.

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