A Study of Subminimal Logics of Negation and Their Modal Companions

Bezhanishvili, Nick; Colacito, Almudena; de Jongh, Dick (2019). A Study of Subminimal Logics of Negation and Their Modal Companions. In: Silva, Alexandra; Staton, Sam; Sutton, Peter; Umbach, Carla (eds.) International Tbilisi Symposium on Logic, Language, and Computation. Lecture Notes in Computer Science: Vol. 11456 (pp. 21-41). Berlin, Heidelberg: Springer Berlin Heidelberg 10.1007/978-3-662-59565-7_2

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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.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Colacito, Almudena

Subjects:

500 Science > 510 Mathematics

ISBN:

978-3-662-59565-7

Series:

Lecture Notes in Computer Science

Publisher:

Springer Berlin Heidelberg

Language:

English

Submitter:

Michel Arthur Bik

Date Deposited:

22 Oct 2019 16:23

Last Modified:

22 Oct 2019 16:50

Publisher DOI:

10.1007/978-3-662-59565-7_2

BORIS DOI:

10.7892/boris.134100

URI:

https://boris.unibe.ch/id/eprint/134100

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