Abstract
We present an algebraic proof of the theorem stating that there are continuum many axiomatic extensions of global consequence associated with modal system E that do not admit the local deduction detachment theorem. We also prove that all these logics lack the finite frame property and have exactly three proper axiomatic extensions, each of which admits the local deduction detachment theorem.
Citation
Krzysztof A. Krawczyk. "Deduction Theorem in Congruential Modal Logics." Notre Dame J. Formal Logic 64 (2) 185 - 196, May 2023. https://doi.org/10.1215/00294527-10670082
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