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Correia Semantics Revisited

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Abstract

Despite a renewed interest in Richard Angell’s logic of analytic containment (\({\mathsf{AC}}\)), the first semantics for \({\mathsf{AC}}\) introduced by Fabrice Correia has remained largely unexamined. This paper describes a reasonable approach to Correia semantics by means of a correspondence with a nine-valued semantics for \({\mathsf{AC}}\). The present inquiry employs this correspondence to provide characterizations of a number of propositional logics intermediate between \({\mathsf{AC}}\) and classical logic. In particular, we examine Correia’s purported characterization of classical logic with respect to his semantics, showing the condition Correia cites in fact characterizes the “logic of paradox” \({\mathsf{LP}}\) and provide a correct characterization. Finally, we consider some remarks on related matters, such as the applicability of the present correspondence to the analysis of the system \({\mathsf{AC}^{\ast}}\) and an intriguing relationship between Correia’s models and articular models for first degree entailment.

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  1. Department of Philosophy, City University of New York Graduate Center, 365 Fifth Avenue, New York, USA

    Thomas Macaulay Ferguson

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  1. Thomas Macaulay Ferguson
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Correspondence to Thomas Macaulay Ferguson.

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Ferguson, T.M. Correia Semantics Revisited. Stud Logica 104, 145–173 (2016). https://doi.org/10.1007/s11225-015-9631-2

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