Metcalfe, George; Tokuda, Naomi (2024). Deciding dependence in logic and algebra. In: Bezhanishvili, Nick; Iemhoff, Rosalie; Yang, Fan (eds.) Dick de Jongh on Intuitionistic and Provability Logics. Outstanding Contributions to Logic: Vol. 28 (pp. 155-173). Springer
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We introduce a universal algebraic generalization of de Jongh's notion of dependence for formulas of intuitionistic propositional logic, relating it to a notion of dependence defined by Marczewski for elements of an algebraic structure. Following ideas of de Jongh and Chagrova, we show how constructive proofs of (weak forms of) uniform interpolation can be used to decide dependence for varieties of abelian l-groups, MV-algebras, semigroups, and modal algebras. We also consider minimal provability results for dependence, obtaining in particular a complete description and decidability of dependence for the variety of lattices.
Item Type: |
Book Section (Book Chapter) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Metcalfe, George, Tokuda, Naomi Maja |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
2211-2758 |
ISBN: |
978-3-031-47920-5 |
Series: |
Outstanding Contributions to Logic |
Publisher: |
Springer |
Language: |
English |
Submitter: |
George Metcalfe |
Date Deposited: |
07 Aug 2024 13:59 |
Last Modified: |
07 Aug 2024 13:59 |
ArXiv ID: |
2106.10100v1 |
BORIS DOI: |
10.48350/199553 |
URI: |
https://boris.unibe.ch/id/eprint/199553 |
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