Approximate Completeness of Hypersequent Calculus for First-Order {\L}ukasiewicz Logic
Logic
2024-12-09 v1
Abstract
Hypersequent calculus G{\L} for first-order {\L}ukasiewicz logic was first introduced by Baaz and Metcalfe, along with a proof of its approximate completeness with respect to standard -semantics. The completeness result was later pointed out by Gerasimov that it only applies to prenex formulas. In this paper, we will present our proof of approximate completeness of G{\L} for arbitrary first-order formulas by generalizing the original completeness proof to hypersequents.
Cite
@article{arxiv.2412.04843,
title = {Approximate Completeness of Hypersequent Calculus for First-Order {\L}ukasiewicz Logic},
author = {Jin Wei},
journal= {arXiv preprint arXiv:2412.04843},
year = {2024}
}