De Morgan-Płonka sums

Thomas Randriamahazaka

doi:10.1007/s11225-024-10111-7

De Morgan-Płonka sums

Thomas Randriamahazaka^*

^*Corresponding author for this work

Philosophy

Research output: Contribution to journal › Article › peer-review

Abstract

This paper develops De Morgan-Płonka sums, which generalise Płonka sums to contexts in which negation is not topically transparent but still respects De Morgan duality. We give a general theory of De Morgan-Płonka sums, on the model of the general theory of Płonka sums. Additionally, we describe free De Morgan-Płonka sums and apply our construction to give an algebraic proof of completeness for Kit Fine’s truthmaker semantics for Angell’s logic of analytic containment.

Original language	English
Number of pages	29
Journal	Studia Logica
Early online date	21 May 2024
DOIs	https://doi.org/10.1007/s11225-024-10111-7
Publication status	E-pub ahead of print - 21 May 2024

Keywords

Plonka sums
De Morgan duality
Nonclassical logics
Algebraic logic
Truth-maker semantics

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10.1007/s11225-024-10111-7Licence: CC BY

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AB - This paper develops De Morgan-Płonka sums, which generalise Płonka sums to contexts in which negation is not topically transparent but still respects De Morgan duality. We give a general theory of De Morgan-Płonka sums, on the model of the general theory of Płonka sums. Additionally, we describe free De Morgan-Płonka sums and apply our construction to give an algebraic proof of completeness for Kit Fine’s truthmaker semantics for Angell’s logic of analytic containment.

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KW - De Morgan duality

KW - Nonclassical logics

KW - Algebraic logic

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De Morgan-Płonka sums

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