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Sequent-Calculi for Metainferential Logics

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Abstract

In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their inferences, but not in their metainferences were considered to be different. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as \(\mathbf {ST}, \mathbf {LP}, \mathbf {K_3}\), and \(\mathbf {TS}\). What is distinctive of these metainferential logics is that they are mixed, i.e. the standard for the premises and the conclusion is not necessarily the same. However, so far, all of these systems have been presented following a semantical standpoint, in terms of valuations based on the Strong Kleene truth-tables. In this article, we provide sound and complete sequent-calculi for the valid inferences and the invalid inferences of the logics \(\mathbf {ST}, \mathbf {LP}, \mathbf {K_3}\) and \(\mathbf {TS}\), and introduce an algorithm that allows obtaining sound and complete sequent-calculi for the global validities and the global invalidities of any metainferential logic of any level.

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Acknowledgements

We would like to thank two anonymous reviewers of this journal for their comments and suggestions which improved the content of the article. Also, we would like to thank the audience of the Workshop on Substructural Logics and Metainferences (Buenos Aires, 2020). Our thanks also go to the members of the Buenos Aires Logic Group, especially to Lucas Rosenblatt for their comments on earlier versions of this manuscript. This paper could not have been written without the financial aid of the National Scientific and Technical Research Council (CONICET). While writing this paper, Federico Pailos enjoyed a Humboldt Research Fellowship for experienced researchers (March 2020 to July 2021).

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  1. IIF-SADAF-CONICET, Buenos Aires, Argentina

    Bruno Da Ré & Federico Pailos

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  1. Bruno Da Ré
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  2. Federico Pailos
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Correspondence to Bruno Da Ré.

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Da Ré, B., Pailos, F. Sequent-Calculi for Metainferential Logics. Stud Logica 110, 319–353 (2022). https://doi.org/10.1007/s11225-021-09967-w

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