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Correia Semantics Revisited

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Meaning and Proscription in Formal Logic

Part of the book series: Trends in Logic ((TREN,volume 49))

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Abstract

In this chapter, the correspondence between the present many-valued semantics for \(\mathsf {AC}\) and those of Correia is revisited and studied in more details. The technique that plays an essential role in proving the completeness of the many-valued semantics for \(\mathsf {AC}\) in Chap. 4 is used to characterize a wide class of first-degree calculi intermediate between \(\mathsf {AC}\) and classical logic in Correia’s setting. This correspondence allows the correction of an incorrect characterization of classical logic made by Correia and leads to the question of how to characterize hybrid systems extending Angell’s \(\mathsf {AC}^{*}\). Finally, we consider whether this correspondence aids in providing an interpretation to Correia’s first semantics for \(\mathsf {AC}\).

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Notes

  1. 1.

    While \(\mathsf {S0}\) (and hence \(\mathsf {S0}_{\mathtt {fde}}\)) has a semantic analysis due to Sylvan and Meyer in [19], the semantics is exceedingly artificial, as the authors freely concede.

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Authors and Affiliations

  1. Cycorp, Inc., Austin, TX, USA

    Thomas Macaulay Ferguson

  2. Saul Kripke Center, New York, NY, 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. (2017). Correia Semantics Revisited. In: Meaning and Proscription in Formal Logic. Trends in Logic, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-70821-8_7

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