On Infinitary Gödel logics
arXiv:1708.07897
Abstract
We study propositional and first-order Gödel 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 Schütte-Tait-style. Initial observations are made regarding truth-value sets other than [0,1].
31 pages, 1 figure