On Infinitary G\"odel logics
Logic
2021-09-07 v4
Abstract
We study propositional and first-order G\"odel logics over infinitary languages which are motivated semantically by corresponding interpretations into the unit interval [0,1]. We provide infinitary Hilbert-style calculi for the particular (propositional and first-order) cases with con-/disjunctions of countable length and prove corresponding completeness theorems by extending the usual Lindenbaum-Tarski construction to the infinitary case for a respective algebraic semantics via complete linear Heyting algebras. We provide infinitary hypersequent calculi and prove corresponding cut-elimination theorems in the Sch\"utte-Tait-style. Initial observations are made regarding truth-value sets other than [0,1].
Keywords
Cite
@article{arxiv.1708.07897,
title = {On Infinitary G\"odel logics},
author = {Nicholas Pischke},
journal= {arXiv preprint arXiv:1708.07897},
year = {2021}
}
Comments
31 pages, 1 figure