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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Abstract
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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