Year: 2026
Type: preprint
Abstract: We present an abstract framework for conservation and translation theorems between logical calculi. Unlike previous approaches, our setting does not require the underlying consequence relations to satisfy structural properties such as cut, allowing in particular for cut-free calculi. Moreover, we study translations between arbitrary calculi rather than only from a stable extension to the original calculus. Translations are formulated at the level of sequents by pairs of functions acting on antecedents and succedents, and the framework is developed for multi-succedent calculi while subsuming the single-succedent case. This yields a uniform treatment of classical results including negative translations, minimality theorems, Orevkov's conservation classes, and a characterisation of the least logic satisfying Kuroda's double negation theorem.
Source: arXiv (Cornell University)
Author: Fellin, Giulio
Institution: University of Verona
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214799545