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Falsification-Aware Semantics and Sequent Calculi for Classical Logic

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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 (N3). In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3 (i.e., a classical variant of N3 is identical to first-order classical logic). 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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Acknowledgments

We would like to thank the anonymous referees for their valuable comments. This research was supported by JSPS KAKENHI Grant Numbers JP18K11171 and JP16KK0007.

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  1. Teikyo University, Faculty of Science and Engineering, Department of Information and Electronic Engineering, Toyosatodai 1-1, Utsunomiya, Tochigi, 320-8551, Japan

    Norihiro Kamide

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  1. Norihiro Kamide
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Correspondence to Norihiro Kamide.

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Kamide, N. Falsification-Aware Semantics and Sequent Calculi for Classical Logic. J Philos Logic 51, 99–126 (2022). https://doi.org/10.1007/s10992-021-09611-x

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