Abstract:The hypersequent calculus $\text{Gﾅ±\forall$, an analytic Gentzen-style proof system of first-order ﾅ「kasiewicz logic, and its approximate completeness have been extensively studied. In this paper, we prove the approximate strong completeness of $\text{Gﾅ±\forall$ by a labelled tableau method. Then we introduce a sequent-level cut rule (s-Cut) and show the approximate strong completeness of $\text{Gﾅ±\forall+(\text{s-Cut})$. As applications, we establish the compactness of approximate $[0, 1]$-consequence, a variant of Gentzen's mid-sequent theorem of $\text{Gﾅ±\forall$ and an approximate Herbrand's theorem of first-order ﾅ「kasiewicz logic.
From: Kai Duo [view email]
[v1]
Tue, 2 Jun 2026 04:21:40 UTC (19 KB)
[v2]
Tue, 14 Jul 2026 15:13:44 UTC (24 KB)
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