PP-2018-09: A Study of Subminimal Logics of Negation and their Modal Companions

PP-2018-09: Bezhanishvili, Nick and Colacito, Almudena and de Jongh, Dick (2018) A Study of Subminimal Logics of Negation and their Modal Companions. [Pre-print] (Submitted)

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We study propositional logical systems arising from the lan- guage of Johansson’s minimal logic and obtained by weakening the re- quirements for the negation operator. Using duality and completeness we prove that there are uncountably many such logical systems. We also give model-theoretic and algebraic definitions of filtration for minimal logic and show that they are dual to each other. These constructions en- sure 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.

Item Type: Pre-print
Report Nr: PP-2018-09
Series Name: Prepublication (PP) Series
Year: 2018
Uncontrolled Keywords: Subminimal Logic, Negation, Modal Companion, Algebraic Logic
Subjects: Logic
Depositing User: Prof. Dick de Jongh
Date Deposited: 15 Apr 2018 15:33
Last Modified: 09 Aug 2019 13:09
URI: https://eprints.illc.uva.nl/id/eprint/1603

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