[2312.03426] Internal and External Calculi: Ordering the Jungle without Being Lost in Translations
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Logic in Computer Science

arXiv:2312.03426 (cs)
[Submitted on 6 Dec 2023]

Title:Internal and External Calculi: Ordering the Jungle without Being Lost in Translations

Authors:Tim S. Lyon, Agata Ciabattoni, Didier Galmiche, Dominique Larchey-Wendling, Daniel Méry, Nicola Olivetti, Revantha Ramanayake
View PDF
Abstract:This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After providing an overview of the logics and proof formalisms under consideration, we show how these sequent-based formalisms can be placed in a hierarchy in terms of the underlying data structure of the sequents. We then discuss how this hierarchy can be traversed using translations. Translating proofs up this hierarchy is found to be relatively easy while translating proofs down the hierarchy is substantially more difficult. Finally, we inspect the prevalent distinction in structural proof theory between 'internal calculi' and 'external calculi'. It is observed that these classes resist a rigorous separation, and we critically assess the properties that (calculi from) these classes are purported to possess.
Subjects: Logic in Computer Science (cs.LO); Logic (math.LO)
Cite as: arXiv:2312.03426 [cs.LO]
  (or arXiv:2312.03426v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2312.03426

Submission history

From: Tim Lyon [view email]
[v1] Wed, 6 Dec 2023 11:17:14 UTC (1,419 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
cs.LO
< prev   |   next >
new | recent | 2023-12
Change to browse by:
cs
math
math.LO

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)