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A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication

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Abstract

We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.

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Acknowledgements

I would like to thank two anonymous referees for their valuable input, as well as Eduardo Barrio, Bruno Da Ré, Thomas Ferguson, Rohan French, Federico Pailos, Lucas Rosenblatt, and the members of the Buenos Aires Logic Group for their comments and suggestions. I am especially thankful to Francesco Paoli for discussing with me many important technical issues that were essential for writing this article. This work was carried out while enjoying a doctoral and later a postdoctoral scholarship from CONICET (The National Scientific and Technical Research Council of Argentina).

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  1. IIF (CONICET-SADAF), Bulnes 642, C1176ABL, Buenos Aires, Argentina

    Damian E. Szmuc

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Correspondence to Damian E. Szmuc.

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Szmuc, D.E. A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication. Stud Logica 109, 791–828 (2021). https://doi.org/10.1007/s11225-020-09926-x

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