A study of subminimal logics of negation and their modal companions
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Publication:6084522
DOI10.1007/978-3-662-59565-7_2zbMATH Open1525.03048arXiv2002.11518OpenAlexW2955527730MaRDI QIDQ6084522
Almudena Colacito, Dick H. J. de Jongh, Nick Bezhanishvili
Publication date: 1 December 2023
Published in: Lecture Notes in Computer Science (Search for Journal in Brave)
Abstract: We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use duality and completeness results to show that there are uncountably many subminimal logics. We also give model-theoretic and algebraic definitions of filtration for minimal logic and show that they are dual to each other. These constructions ensure that the propositional minimal logic has the finite model property. Finally, we define and investigate bi-modal companions with non-normal modal operators for some relevant subminimal systems, and give infinite axiomatizations for these bi-modal companions.
Full work available at URL: https://arxiv.org/abs/2002.11518
Modal logic (including the logic of norms) (03B45) Subsystems of classical logic (including intuitionistic logic) (03B20) Paraconsistent logics (03B53)
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