Angell and McCall Meet Wansing

Studia Logica 112 (1):141-165 (2024)
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Abstract

In this paper, we introduce a new logic, which we call AM3. It is a connexive logic that has several interesting properties, among them being strongly connexive and validating the Converse Boethius Thesis. These two properties are rather characteristic of the difference between, on the one hand, Angell and McCall’s CC1 and, on the other, Wansing’s C. We will show that in other aspects, as well, AM3 combines what are, arguably, the strengths of both CC1 and C. It also allows us an interesting look at how connexivity and the intuitionistic understanding of negation relate to each other. However, some problems remain, and we end by pointing to a large family of weaker logics that AM3 invites us to further explore.

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References found in this work

Connexive implication.Storrs Mccall - 1966 - Journal of Symbolic Logic 31 (3):415-433.
Semantics for Pure Theories of Connexive Implication.Yale Weiss - 2022 - Review of Symbolic Logic 15 (3):591-606.
Negation as Cancellation, Connexive Logic, and qLPm.Heinrich Wansing - 2018 - Australasian Journal of Logic 15 (2):476-488.
A propositional logic with subjunctive conditionals.R. B. Angell - 1962 - Journal of Symbolic Logic 27 (3):327-343.
The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.

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