Abstract
In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics \(\mathsf {E}\), \(\mathsf {M}\), \(\mathsf {MC}\), \(\mathsf {EN}\), \(\mathsf {MN}\) have that property. In particular, these logics have uniform interpolation. Although for some of them the latter is known, the fact that they have uniform Lyndon interpolation is new. Also, the proof-theoretic proofs of these facts are new, as well as the constructive way to explicitly compute the interpolants that they provide. It is also shown that the non-normal modal logics \(\mathsf {EC}\) and \(\mathsf {ECN}\) do not have Craig interpolation, and whence no uniform (Lyndon) interpolation.
Support by the Netherlands Organisation for Scientific Research under grant 639.073.807 is gratefully acknowledged.
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Notes
- 1.
The label \(\diamond \) has nothing to do with the modal operator \(\Diamond =\lnot \Box \lnot \).
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Acknowledgements
We thank Iris van der Giessen for fruitful discussions on the topic of this paper and three referees for comments that helped improving the paper.
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Akbar Tabatabai, A., Iemhoff, R., Jalali, R. (2021). Uniform Lyndon Interpolation for Basic Non-normal Modal Logics. In: Silva, A., Wassermann, R., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2021. Lecture Notes in Computer Science(), vol 13038. Springer, Cham. https://doi.org/10.1007/978-3-030-88853-4_18
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