Varieties of Modal Algebras Without the Congruence Extension Property
Abstract
In a recent paper, Krawczyk proved that there are continuum many axiomatic extensions of global consequence associated with the modal system $E$ that do not admit the local deduction detachment theorem. In algebraic parlance, he showed that there are continuum many varieties of modal algebras lacking the congruence extension property. In this paper, we extend Krawczyk's results and construct a continuum of varieties of modal algebras that do not have the congruence extension property, but that do admit other, logically relevant properties, such as monotonicity, extensiveness, idempotency, normality, etc. This gives a continuum of axiomatic extensions of the corresponding modal systems not having the local deduction detachment theorem.
Fields of Study & Subjects
Advanced Algebra and Logic
Logic
programming
and type systems
Formal Methods in Verification
Publication details
- Journal / source
- Notre Dame Journal of Formal Logic
- Publisher
- Duke University Press
- Volume
- 67
- Issue
- 2
- Pages
- 159-176
- Publication date
- 1 May 2026
- Language
- EN