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Andreas Fjellstad | Structural proof theory for first-order weak Kleene logics | Journal of Applied Non-Classical Logics

Structural proof theory for first-order weak Kleene logics

Andreas Fjellstad

ABSTRACT

This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.

KEYWORDS: Sequent calculus, weak Kleene quantifiers, cut-elimination, completeness, structural proof theory