Journal of Philosophical Logic 51 (1):99-126 (2022)

Abstract
In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent calculi are constructed based on a falsification-aware setting for first-order Nelson constructive three-valued logic. In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3. The completeness and cut-elimination theorems for the proposed semantics and sequent calculi are proved using Schütte’s method. Similar results for the propositional case are also obtained.
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DOI 10.1007/s10992-021-09611-x
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References found in this work BETA

The Collected Papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam: North-Holland Pub. Co..
Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructible Falsity and Inexact Predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.

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