English

Approximate Completeness of Hypersequent Calculus for First-Order {\L}ukasiewicz Logic

Logic 2024-12-09 v1

Abstract

Hypersequent calculus G{\L}\forall 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 [0,1][0,1]-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}\forall 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}
}
R2 v1 2026-06-28T20:25:16.383Z